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प्रचलित समस्याएं

रैंक	विषय	समस्या	फॉर्मेट की गई समस्या
7901	सर्वसमिका जाँच करें	1/(cos(x)-sin(x))=cos(x)+sin(x)	$\frac{1}{\cos (x) - \sin (x)} = \cos (x) + \sin (x)$ $\frac{1}{\cos (x) - \sin (x)} = \cos (x) + \sin (x)$
7902	सर्वसमिका जाँच करें	1/(1+cos(x))-1/(1-cos(x))=-2csc(x)cot(x)	$\frac{1}{1 + \cos (x)} - \frac{1}{1 - \cos (x)} = - 2 \csc (x) \cot (x)$ $\frac{1}{1 + \cos (x)} - \frac{1}{1 - \cos (x)} = - 2 \csc (x) \cot (x)$
7903	सर्वसमिका जाँच करें	1/(1+cos(x))+1/(1-cos(x))=2csc(x)^2	$\frac{1}{1 + \cos (x)} + \frac{1}{1 - \cos (x)} = 2 \csc^{2} (x)$ $\frac{1}{1 + \cos (x)} + \frac{1}{1 - \cos (x)} = 2 \csc^{2} (x)$
7904	सर्वसमिका जाँच करें	(1+sin(t))/(cos(t))=(cos(t))/(1-sin(t))	$\frac{1 + \sin (t)}{\cos (t)} = \frac{\cos (t)}{1 - \sin (t)}$ $\frac{1 + \sin (t)}{\cos (t)} = \frac{\cos (t)}{1 - \sin (t)}$
7905	सर्वसमिका जाँच करें	(1+tan(u))/(1-tan(u))=(cot(u)+1)/(cot(u)-1)	$\frac{1 + \tan (u)}{1 - \tan (u)} = \frac{\cot (u) + 1}{\cot (u) - 1}$ $\frac{1 + \tan (u)}{1 - \tan (u)} = \frac{\cot (u) + 1}{\cot (u) - 1}$
7906	सर्वसमिका जाँच करें	(1+tan(y))/(1+cot(y))=(sec(y))/(csc(y))	$\frac{1 + \tan (y)}{1 + \cot (y)} = \frac{\sec (y)}{\csc (y)}$ $\frac{1 + \tan (y)}{1 + \cot (y)} = \frac{\sec (y)}{\csc (y)}$
7907	सर्वसमिका जाँच करें	(1+cot(x))/(1+tan(x))=cot(x)	$\frac{1 + \cot (x)}{1 + \tan (x)} = \cot (x)$ $\frac{1 + \cot (x)}{1 + \tan (x)} = \cot (x)$
7908	सर्वसमिका जाँच करें	(1-csc(x))/(1-sin(x))=-csc(x)	$\frac{1 - \csc (x)}{1 - \sin (x)} = - \csc (x)$ $\frac{1 - \csc (x)}{1 - \sin (x)} = - \csc (x)$
7909	सर्वसमिका जाँच करें	(1-sin(2x))/(sin(x)-cos(x))=sin(x)-cos(x)	$\frac{1 - \sin (2 x)}{\sin (x) - \cos (x)} = \sin (x) - \cos (x)$ $\frac{1 - \sin (2 x)}{\sin (x) - \cos (x)} = \sin (x) - \cos (x)$
7910	सर्वसमिका जाँच करें	(sec(u)-tan(u))(sec(u)+tan(u))=1	$(\sec (u) - \tan (u)) (\sec (u) + \tan (u)) = 1$ $(\sec (u) - \tan (u)) (\sec (u) + \tan (u)) = 1$
7911	सर्वसमिका जाँच करें	(cot(x)sec(x))/(csc(x))=1	$\frac{\cot (x) \sec (x)}{\csc (x)} = 1$ $\frac{\cot (x) \sec (x)}{\csc (x)} = 1$
7912	सर्वसमिका जाँच करें	(cos(2x)+sin(2x))^2=1+sin(4x)	${(\cos (2 x) + \sin (2 x))}^{2} = 1 + \sin (4 x)$ ${(\cos (2 x) + \sin (2 x))}^{2} = 1 + \sin (4 x)$
7913	सर्वसमिका जाँच करें	(sin(x)-cos(x))^2=1+sin(2x)	${(\sin (x) - \cos (x))}^{2} = 1 + \sin (2 x)$ ${(\sin (x) - \cos (x))}^{2} = 1 + \sin (2 x)$
7914	सर्वसमिका जाँच करें	(cot(45-x)^2-1)/(cot(45-x)^2+1)=sin(2x)	$\frac{\cot^{2} (45 - x) - 1}{\cot^{2} (45 - x) + 1} = \sin (2 x)$ $\frac{\cot^{2} (45 - x) - 1}{\cot^{2} (45 - x) + 1} = \sin (2 x)$
7915	सर्वसमिका जाँच करें	(cot(t)^3)/(csc(t))=cos(t)(csc(t)^2-1)	$\frac{\cot^{3} (t)}{\csc (t)} = \cos (t) (\csc^{2} (t) - 1)$ $\frac{\cot^{3} (t)}{\csc (t)} = \cos (t) (\csc^{2} (t) - 1)$
7916	सर्वसमिका जाँच करें	(cos(t)^2)/(sin(t))=csc(t)-sin(t)	$\frac{\cos^{2} (t)}{\sin (t)} = \csc (t) - \sin (t)$ $\frac{\cos^{2} (t)}{\sin (t)} = \csc (t) - \sin (t)$
7917	सर्वसमिका जाँच करें	(1-cot(x)^2)/(1+cot(x)^2)+2cos(x)^2=1	$\frac{1 - \cot^{2} (x)}{1 + \cot^{2} (x)} + 2 \cos^{2} (x) = 1$ $\frac{1 - \cot^{2} (x)}{1 + \cot^{2} (x)} + 2 \cos^{2} (x) = 1$
7918	सर्वसमिका जाँच करें	(1-sin(x)^2)/(1-sin(x))=(csc(x)+1)/(csc(x))	$\frac{1 - \sin^{2} (x)}{1 - \sin (x)} = \frac{\csc (x) + 1}{\csc (x)}$ $\frac{1 - \sin^{2} (x)}{1 - \sin (x)} = \frac{\csc (x) + 1}{\csc (x)}$
7919	सर्वसमिका जाँच करें	(1-tan(x)^2)/(1+tan(x)^2)=cos(2x)	$\frac{1 - \tan^{2} (x)}{1 + \tan^{2} (x)} = \cos (2 x)$ $\frac{1 - \tan^{2} (x)}{1 + \tan^{2} (x)} = \cos (2 x)$
7920	सर्वसमिका जाँच करें	(sec(x)^2)/(sec(x)^2-1)=csc(x)^2	$\frac{\sec^{2} (x)}{\sec^{2} (x) - 1} = \csc^{2} (x)$ $\frac{\sec^{2} (x)}{\sec^{2} (x) - 1} = \csc^{2} (x)$
7921	सर्वसमिका जाँच करें	(sec(t)^2)/(tan(t))=cot(t)+tan(t)	$\frac{\sec^{2} (t)}{\tan (t)} = \cot (t) + \tan (t)$ $\frac{\sec^{2} (t)}{\tan (t)} = \cot (t) + \tan (t)$
7922	सर्वसमिका जाँच करें	2cos(4x)^2-1=0	$2 \cos^{2} (4 x) - 1 = 0$ $2 \cos^{2} (4 x) - 1 = 0$
7923	सर्वसमिका जाँच करें	2cos(x)^2-cos(x)=1	$2 \cos^{2} (x) - \cos (x) = 1$ $2 \cos^{2} (x) - \cos (x) = 1$
7924	सर्वसमिका जाँच करें	2sin(x)^2+sin(x-1)=0	$2 \sin^{2} (x) + \sin (x - 1) = 0$ $2 \sin^{2} (x) + \sin (x - 1) = 0$
7925	सर्वसमिका जाँच करें	2cot(2x)=cot(x)-tan(x)	$2 \cot (2 x) = \cot (x) - \tan (x)$ $2 \cot (2 x) = \cot (x) - \tan (x)$
7926	सर्वसमिका जाँच करें	2csc(2x)=sec(x)csc(x)	$2 \csc (2 x) = \sec (x) \csc (x)$ $2 \csc (2 x) = \sec (x) \csc (x)$
7927	सर्वसमिका जाँच करें	2sin(x)^2=sin(x)	$2 \sin^{2} (x) = \sin (x)$ $2 \sin^{2} (x) = \sin (x)$
7928	सर्वसमिका जाँच करें	2sin(2x)cos(x)+3sin(x)=0	$2 \sin (2 x) \cos (x) + 3 \sin (x) = 0$ $2 \sin (2 x) \cos (x) + 3 \sin (x) = 0$
7929	सर्वसमिका जाँच करें	2sin(x)- 3=0 का वर्गमूल	$2 \sin (x) - \sqrt{3} = 0$ $2 \sin (x) - \sqrt{3} = 0$
7930	सर्वसमिका जाँच करें	5cos(B)^2-5sin(B)^2=10cos(B)^2-5	$5 \cos^{2} (B) - 5 \sin^{2} (B) = 10 \cos^{2} (B) - 5$ $5 \cos^{2} (B) - 5 \sin^{2} (B) = 10 \cos^{2} (B) - 5$
7931	सर्वसमिका जाँच करें	3sin(x)-2cos(x)=1	$3 \sin (x) - 2 \cos (x) = 1$ $3 \sin (x) - 2 \cos (x) = 1$
7932	सर्वसमिका जाँच करें	cos(x)(sec(x)-cos(x))=sin(x)^2	$\cos (x) (\sec (x) - \cos (x)) = \sin^{2} (x)$ $\cos (x) (\sec (x) - \cos (x)) = \sin^{2} (x)$
7933	सर्वसमिका जाँच करें	700tan(41)=b+h	$700 \tan (41) = b + h$ $700 \tan (41) = b + h$
7934	सर्वसमिका जाँच करें	cot(-x)sin(-x)=cos(x)	$\cot (- x) \sin (- x) = \cos (x)$ $\cot (- x) \sin (- x) = \cos (x)$
7935	सर्वसमिका जाँच करें	csc(x/2)sec(x/2)=csc(x)	$\csc (\frac{x}{2}) \sec (\frac{x}{2}) = \csc (x)$ $\csc (\frac{x}{2}) \sec (\frac{x}{2}) = \csc (x)$
7936	सर्वसमिका जाँच करें	csc(x)=1/(sin(x))	$\csc (x) = \frac{1}{\sin (x)}$ $\csc (x) = \frac{1}{\sin (x)}$
7937	सर्वसमिका जाँच करें	csc(2A)-cot(2A)=tan(A)	$\csc (2 A) - \cot (2 A) = \tan (A)$ $\csc (2 A) - \cot (2 A) = \tan (A)$
7938	सर्वसमिका जाँच करें	csc(A)sin(2A)-sec(A)=cos(2A)sec(A)	$\csc (A) \sin (2 A) - \sec (A) = \cos (2 A) \sec (A)$ $\csc (A) \sin (2 A) - \sec (A) = \cos (2 A) \sec (A)$
7939	सर्वसमिका जाँच करें	cot(x)*sec(x)=csc(x)	$\cot (x) \cdot \sec (x) = \csc (x)$ $\cot (x) \cdot \sec (x) = \csc (x)$
7940	सर्वसमिका जाँच करें	cot(x)+sec(x)csc(x)=(tan(x))/(1+cos(x))+(sin(x))/(1-cos(x))	$\cot (x) + \sec (x) \csc (x) = \frac{\tan (x)}{1 + \cos (x)} + \frac{\sin (x)}{1 - \cos (x)}$ $\cot (x) + \sec (x) \csc (x) = \frac{\tan (x)}{1 + \cos (x)} + \frac{\sin (x)}{1 - \cos (x)}$
7941	सर्वसमिका जाँच करें	cos(x-pi/4)=( 2)/2*(cos(x)+sin(x)) का वर्गमूल	$\cos (x - \frac{π}{4}) = \frac{\sqrt{2}}{2} \cdot (\cos (x) + \sin (x))$ $\cos (x - \frac{π}{4}) = \frac{\sqrt{2}}{2} \cdot (\cos (x) + \sin (x))$
7942	सर्वसमिका जाँच करें	cos(x)=sin(x)cot(x)	$\cos (x) = \sin (x) \cot (x)$ $\cos (x) = \sin (x) \cot (x)$
7943	सर्वसमिका जाँच करें	cos(x)cos(y)=1/2*(sin(x+y)+sin(x-y))	$\cos (x) \cos (y) = \frac{1}{2} \cdot (\sin (x + y) + \sin (x - y))$ $\cos (x) \cos (y) = \frac{1}{2} \cdot (\sin (x + y) + \sin (x - y))$
7944	सर्वसमिका जाँच करें	cos(x)cos(2x)-sin(x)sin(2x)=0	$\cos (x) \cos (2 x) - \sin (x) \sin (2 x) = 0$ $\cos (x) \cos (2 x) - \sin (x) \sin (2 x) = 0$
7945	सर्वसमिका जाँच करें	cos((3pi)/2-x)=-sin(x)	$\cos (\frac{3 π}{2} - x) = - \sin (x)$ $\cos (\frac{3 π}{2} - x) = - \sin (x)$
7946	सर्वसमिका जाँच करें	cos((5pi)/3+x)+sin((7pi)/6+x)=0	$\cos (\frac{5 π}{3} + x) + \sin (\frac{7 π}{6} + x) = 0$ $\cos (\frac{5 π}{3} + x) + \sin (\frac{7 π}{6} + x) = 0$
7947	सर्वसमिका जाँच करें	cos(2x-pi/2)=1	$\cos (2 x - \frac{π}{2}) = 1$ $\cos (2 x - \frac{π}{2}) = 1$
7948	सर्वसमिका जाँच करें	cos(2x)=2-2sin(x)^2	$\cos (2 x) = 2 - 2 \sin^{2} (x)$ $\cos (2 x) = 2 - 2 \sin^{2} (x)$
7949	सर्वसमिका जाँच करें	cos(2x)=( 2)/2 का वर्गमूल	$\cos (2 x) = \frac{\sqrt{2}}{2}$ $\cos (2 x) = \frac{\sqrt{2}}{2}$
7950	सर्वसमिका जाँच करें	cos(2x)=(2-sec(x)^2)/(sec(x)^2)	$\cos (2 x) = \frac{2 - \sec^{2} (x)}{\sec^{2} (x)}$ $\cos (2 x) = \frac{2 - \sec^{2} (x)}{\sec^{2} (x)}$
7951	सर्वसमिका जाँच करें	cos(2x)=cos(x)	$\cos (2 x) = \cos (x)$ $\cos (2 x) = \cos (x)$
7952	सर्वसमिका जाँच करें	cos(2x)=cos(x)-1	$\cos (2 x) = \cos (x) - 1$ $\cos (2 x) = \cos (x) - 1$
7953	सर्वसमिका जाँच करें	cos(2x)=2cos(x)^2-1	$\cos (2 x) = 2 \cos^{2} (x) - 1$ $\cos (2 x) = 2 \cos^{2} (x) - 1$
7954	सर्वसमिका जाँच करें	cos(4x)-cos(6x)=0	$\cos (4 x) - \cos (6 x) = 0$ $\cos (4 x) - \cos (6 x) = 0$
7955	सर्वसमिका जाँच करें	cos(pi-x)+sin(pi/2+x)=0	$\cos (π - x) + \sin (\frac{π}{2} + x) = 0$ $\cos (π - x) + \sin (\frac{π}{2} + x) = 0$
7956	सर्वसमिका जाँच करें	cos(3t)=cos(t)^3-3sin(t)^2cos(t)	$\cos (3 t) = \cos^{3} (t) - 3 \sin^{2} (t) \cos (t)$ $\cos (3 t) = \cos^{3} (t) - 3 \sin^{2} (t) \cos (t)$
7957	सर्वसमिका जाँच करें	(sin(x))/(1+cos(x))+(cos(x))/(sin(x))=csc(x)	$\frac{\sin (x)}{1 + \cos (x)} + \frac{\cos (x)}{\sin (x)} = \csc (x)$ $\frac{\sin (x)}{1 + \cos (x)} + \frac{\cos (x)}{\sin (x)} = \csc (x)$
7958	सर्वसमिका जाँच करें	sec(t)^4-tan(t)^4=1+2tan(t)^2	$\sec^{4} (t) - \tan^{4} (t) = 1 + 2 \tan^{2} (t)$ $\sec^{4} (t) - \tan^{4} (t) = 1 + 2 \tan^{2} (t)$
7959	सर्वसमिका जाँच करें	(sec(x))/(1+sec(x))=1/(cos(x)+1)	$\frac{\sec (x)}{1 + \sec (x)} = \frac{1}{\cos (x) + 1}$ $\frac{\sec (x)}{1 + \sec (x)} = \frac{1}{\cos (x) + 1}$
7960	सर्वसमिका जाँच करें	(sec(t)-1)/(tan(t))=(tan(t))/(sec(t)+1)	$\frac{\sec (t) - 1}{\tan (t)} = \frac{\tan (t)}{\sec (t) + 1}$ $\frac{\sec (t) - 1}{\tan (t)} = \frac{\tan (t)}{\sec (t) + 1}$
7961	सर्वसमिका जाँच करें	(sec(x)-1)/(1-cos(x))=sec(x)	$\frac{\sec (x) - 1}{1 - \cos (x)} = \sec (x)$ $\frac{\sec (x) - 1}{1 - \cos (x)} = \sec (x)$
7962	सर्वसमिका जाँच करें	(sec(x)-1)/(tan(x))=(tan(x))/(sec(x)+1)	$\frac{\sec (x) - 1}{\tan (x)} = \frac{\tan (x)}{\sec (x) + 1}$ $\frac{\sec (x) - 1}{\tan (x)} = \frac{\tan (x)}{\sec (x) + 1}$
7963	सर्वसमिका जाँच करें	(sec(x))/(csc(x))+(sin(x))/(cos(x))=2tan(x)	$\frac{\sec (x)}{\csc (x)} + \frac{\sin (x)}{\cos (x)} = 2 \tan (x)$ $\frac{\sec (x)}{\csc (x)} + \frac{\sin (x)}{\cos (x)} = 2 \tan (x)$
7964	सर्वसमिका जाँच करें	(sin(2x))/(sin(x))-(cos(2x))/(cos(x))=sec(x)	$\frac{\sin (2 x)}{\sin (x)} - \frac{\cos (2 x)}{\cos (x)} = \sec (x)$ $\frac{\sin (2 x)}{\sin (x)} - \frac{\cos (2 x)}{\cos (x)} = \sec (x)$
7965	सर्वसमिका जाँच करें	(sin(t))/(csc(t))+(cos(t))/(sec(t))=1	$\frac{\sin (t)}{\csc (t)} + \frac{\cos (t)}{\sec (t)} = 1$ $\frac{\sin (t)}{\csc (t)} + \frac{\cos (t)}{\sec (t)} = 1$
7966	सर्वसमिका जाँच करें	(sin(3x)-sin(x))/(cos(3x)+cos(x))=tan(x)	$\frac{\sin (3 x) - \sin (x)}{\cos (3 x) + \cos (x)} = \tan (x)$ $\frac{\sin (3 x) - \sin (x)}{\cos (3 x) + \cos (x)} = \tan (x)$
7967	सर्वसमिका जाँच करें	(sin(4x))/(sin(x))=4cos(x)cos(2x)	$\frac{\sin (4 x)}{\sin (x)} = 4 \cos (x) \cos (2 x)$ $\frac{\sin (4 x)}{\sin (x)} = 4 \cos (x) \cos (2 x)$
7968	सर्वसमिका जाँच करें	csc(x)^5-4csc(x)=0	$\csc^{5} (x) - 4 \csc (x) = 0$ $\csc^{5} (x) - 4 \csc (x) = 0$
7969	सर्वसमिका जाँच करें	(csc(x)-1)/(cot(x))=(cot(x))/(csc(x)+1)	$\frac{\csc (x) - 1}{\cot (x)} = \frac{\cot (x)}{\csc (x) + 1}$ $\frac{\csc (x) - 1}{\cot (x)} = \frac{\cot (x)}{\csc (x) + 1}$
7970	सर्वसमिका जाँच करें	csc(x)^2-cos(x)^2csc(x)^2=1	$\csc^{2} (x) - \cos^{2} (x) \csc^{2} (x) = 1$ $\csc^{2} (x) - \cos^{2} (x) \csc^{2} (x) = 1$
7971	सर्वसमिका जाँच करें	csc(x)^2sec(x)=sec(x)+csc(x)cot(x)	$\csc^{2} (x) \sec (x) = \sec (x) + \csc (x) \cot (x)$ $\csc^{2} (x) \sec (x) = \sec (x) + \csc (x) \cot (x)$
7972	सर्वसमिका जाँच करें	csc(x)^2-cot(x)^2=1	$\csc^{2} (x) - \cot^{2} (x) = 1$ $\csc^{2} (x) - \cot^{2} (x) = 1$
7973	सर्वसमिका जाँच करें	cot(x)^2+csc(x)^2=1+2cot(x)^2	$\cot^{2} (x) + \csc^{2} (x) = 1 + 2 \cot^{2} (x)$ $\cot^{2} (x) + \csc^{2} (x) = 1 + 2 \cot^{2} (x)$
7974	सर्वसमिका जाँच करें	(csc(x)+cot(x))/(tan(x)+sin(x))=csc(x)cot(x)	$\frac{\csc (x) + \cot (x)}{\tan (x) + \sin (x)} = \csc (x) \cot (x)$ $\frac{\csc (x) + \cot (x)}{\tan (x) + \sin (x)} = \csc (x) \cot (x)$
7975	सर्वसमिका जाँच करें	cos(x)^4-sin(x)^4=1	$\cos^{4} (x) - \sin^{4} (x) = 1$ $\cos^{4} (x) - \sin^{4} (x) = 1$
7976	सर्वसमिका जाँच करें	(cot(x)-1)/(cot(x)+1)=(1-tan(x))/(1+tan(x))	$\frac{\cot (x) - 1}{\cot (x) + 1} = \frac{1 - \tan (x)}{1 + \tan (x)}$ $\frac{\cot (x) - 1}{\cot (x) + 1} = \frac{1 - \tan (x)}{1 + \tan (x)}$
7977	सर्वसमिका जाँच करें	(tan(x)^3-1)/(tan(x)-1)=sec(x)^2+tan(x)	$\frac{\tan^{3} (x) - 1}{\tan (x) - 1} = \sec^{2} (x) + \tan (x)$ $\frac{\tan^{3} (x) - 1}{\tan (x) - 1} = \sec^{2} (x) + \tan (x)$
7978	सर्वसमिका जाँच करें	(tan(x)+cot(x))/(csc(x))=sec(x)	$\frac{\tan (x) + \cot (x)}{\csc (x)} = \sec (x)$ $\frac{\tan (x) + \cot (x)}{\csc (x)} = \sec (x)$
7979	सर्वसमिका जाँच करें	1-2cos(x)^2=(tan(x)^2-1)/(tan(x)^2+1)	$1 - 2 \cos^{2} (x) = \frac{\tan^{2} (x) - 1}{\tan^{2} (x) + 1}$ $1 - 2 \cos^{2} (x) = \frac{\tan^{2} (x) - 1}{\tan^{2} (x) + 1}$
7980	सर्वसमिका जाँच करें	sin(t)^3+cos(t)^3+sin(t)cos(t)^2+sin(t)^2cos(t)=sin(t)+cos(t)	$\sin^{3} (t) + \cos^{3} (t) + \sin (t) \cos^{2} (t) + \sin^{2} (t) \cos (t) = \sin (t) + \cos (t)$ $\sin^{3} (t) + \cos^{3} (t) + \sin (t) \cos^{2} (t) + \sin^{2} (t) \cos (t) = \sin (t) + \cos (t)$
7981	सर्वसमिका जाँच करें	(tan(x))/(1+cos(x))+(sin(x))/(1-cos(x))=cot(x)+sec(x)csc(x)	$\frac{\tan (x)}{1 + \cos (x)} + \frac{\sin (x)}{1 - \cos (x)} = \cot (x) + \sec (x) \csc (x)$ $\frac{\tan (x)}{1 + \cos (x)} + \frac{\sin (x)}{1 - \cos (x)} = \cot (x) + \sec (x) \csc (x)$
7982	सर्वसमिका जाँच करें	(tan(x))/(sec(x))+(cot(x))/(csc(x))=sin(x)+cos(x)	$\frac{\tan (x)}{\sec (x)} + \frac{\cot (x)}{\csc (x)} = \sin (x) + \cos (x)$ $\frac{\tan (x)}{\sec (x)} + \frac{\cot (x)}{\csc (x)} = \sin (x) + \cos (x)$
7983	सर्वसमिका जाँच करें	(tan(x))/(sec(x)-1)=(sec(x)+1)/(tan(x))	$\frac{\tan (x)}{\sec (x) - 1} = \frac{\sec (x) + 1}{\tan (x)}$ $\frac{\tan (x)}{\sec (x) - 1} = \frac{\sec (x) + 1}{\tan (x)}$
7984	सर्वसमिका जाँच करें	sin(x)^4-cos(x)^4=1-2cos(x)^2	$\sin^{4} (x) - \cos^{4} (x) = 1 - 2 \cos^{2} (x)$ $\sin^{4} (x) - \cos^{4} (x) = 1 - 2 \cos^{2} (x)$
7985	सर्वसमिका जाँच करें	(tan(x)+sec(x)-1)/(tan(x)-sec(x)+1)=tan(x)+sec(x)	$\frac{\tan (x) + \sec (x) - 1}{\tan (x) - \sec (x) + 1} = \tan (x) + \sec (x)$ $\frac{\tan (x) + \sec (x) - 1}{\tan (x) - \sec (x) + 1} = \tan (x) + \sec (x)$
7986	सर्वसमिका जाँच करें	(tan(2x)+cot(2x))/(csc(2x))=sec(2x)	$\frac{\tan (2 x) + \cot (2 x)}{\csc (2 x)} = \sec (2 x)$ $\frac{\tan (2 x) + \cot (2 x)}{\csc (2 x)} = \sec (2 x)$
7987	सर्वसमिका जाँच करें	(sin(x)+tan(x))/(1+sec(x))=sin(x)	$\frac{\sin (x) + \tan (x)}{1 + \sec (x)} = \sin (x)$ $\frac{\sin (x) + \tan (x)}{1 + \sec (x)} = \sin (x)$
7988	सर्वसमिका जाँच करें	(sin(x)+1)/(sin(x))=1+csc(x)	$\frac{\sin (x) + 1}{\sin (x)} = 1 + \csc (x)$ $\frac{\sin (x) + 1}{\sin (x)} = 1 + \csc (x)$
7989	सर्वसमिका जाँच करें	(sin(x))/(sin(x)-cos(x))=1/(1-cot(x))	$\frac{\sin (x)}{\sin (x) - \cos (x)} = \frac{1}{1 - \cot (x)}$ $\frac{\sin (x)}{\sin (x) - \cos (x)} = \frac{1}{1 - \cot (x)}$
7990	सर्वसमिका जाँच करें	(sin(x))/(cos(x)+1)+(cos(x)-1)/(sin(x))=0	$\frac{\sin (x)}{\cos (x) + 1} + \frac{\cos (x) - 1}{\sin (x)} = 0$ $\frac{\sin (x)}{\cos (x) + 1} + \frac{\cos (x) - 1}{\sin (x)} = 0$
7991	सर्वसमिका जाँच करें	(sin(x)-cos(x))/(sin(x))+(cos(x)-sin(x))/(cos(x))=2-sec(x)csc(x)	$\frac{\sin (x) - \cos (x)}{\sin (x)} + \frac{\cos (x) - \sin (x)}{\cos (x)} = 2 - \sec (x) \csc (x)$ $\frac{\sin (x) - \cos (x)}{\sin (x)} + \frac{\cos (x) - \sin (x)}{\cos (x)} = 2 - \sec (x) \csc (x)$
7992	सर्वसमिका जाँच करें	(sin(x+y))/(cos(x)cos(y))=tan(x)+tan(y)	$\frac{\sin (x + y)}{\cos (x) \cos (y)} = \tan (x) + \tan (y)$ $\frac{\sin (x + y)}{\cos (x) \cos (y)} = \tan (x) + \tan (y)$
7993	बिल्कुल ठीक मान ज्ञात कीजिये	(340)^2+(500)^2-2340500cos(130)	${(340)}^{2} + {(500)}^{2} - 2 \cdot 340 \cdot 500 \cos (130)$ ${(340)}^{2} + {(500)}^{2} - 2 \cdot 340 \cdot 500 \cos (130)$
7994	बिल्कुल ठीक मान ज्ञात कीजिये	(tan(45)+tan(60))^2	${(\tan (45) + \tan (60))}^{2}$ ${(\tan (45) + \tan (60))}^{2}$
7995	बिल्कुल ठीक मान ज्ञात कीजिये	1/(sin(1))	$\frac{1}{\sin (1)}$ $\frac{1}{\sin (1)}$
7996	बिल्कुल ठीक मान ज्ञात कीजिये	1/(tan(30))	$\frac{1}{\tan (30)}$ $\frac{1}{\tan (30)}$
7997	त्रिकोणमितीय व्यंजक का प्रसार कीजिये।	3sin(2x)	$3 \sin (2 x)$ $3 \sin (2 x)$
7998	बिल्कुल ठीक मान ज्ञात कीजिये	(30)(200)cos(35)	$(30) (200) \cos (35)$ $(30) (200) \cos (35)$
7999	सर्वसमिका जाँच करें	y=tan(x+pi/2)	$y = \tan (x + \frac{π}{2})$ $y = \tan (x + \frac{π}{2})$
8000	बिल्कुल ठीक मान ज्ञात कीजिये	(1-cos(330))/(sin(330))	$\frac{1 - \cos (330)}{\sin (330)}$ $\frac{1 - \cos (330)}{\sin (330)}$