Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
4501	Simplify	(cos(x))/(1-tan(x))+(sin(x))/(1-cot(x))	$\frac{\cos (x)}{1 - \tan (x)} + \frac{\sin (x)}{1 - \cot (x)}$
4502	Simplify	(-5pi)/6	$\frac{- 5 π}{6}$
4503	Simplify	3/(sec(x)-tan(x))	$\frac{3}{\sec (x) - \tan (x)}$
4504	Simplify	((1-cos(x))(1+cos(x)))/((1-sin(x))(1+sin(x)))	$\frac{(1 - \cos (x)) (1 + \cos (x))}{(1 - \sin (x)) (1 + \sin (x))}$
4505	Simplify	(1-sin(x))^2	${(1 - \sin (x))}^{2}$
4506	Simplify	(cos(x)^2)/(cot(x)^2)	$\frac{\cos^{2} (x)}{\cot^{2} (x)}$
4507	Simplify	(sec(x)^2-tan(x)^2)/(cot(x)^2-csc(x)^2)	$\frac{\sec^{2} (x) - \tan^{2} (x)}{\cot^{2} (x) - \csc^{2} (x)}$
4508	Simplify	(sec(x)^2)/(tan(x))-tan(x)	$\frac{\sec^{2} (x)}{\tan (x)} - \tan (x)$
4509	Simplify	(sin(x)^2-1)/(cos(-x))	$\frac{\sin^{2} (x) - 1}{\cos (- x)}$
4510	Simplify	(x+i)^2-(x-i)^2	${(x + i)}^{2} - {(x - i)}^{2}$
4511	Simplify	(sin(a)-cos(a))^2	${(\sin (a) - \cos (a))}^{2}$
4512	Simplify	(1-sin(x)^2)/(csc(x)^2-1)	$\frac{1 - \sin^{2} (x)}{\csc^{2} (x) - 1}$
4513	Simplify	(sin(A)^4-cos(A)^4)/(cos(A)-sin(A))	$\frac{\sin^{4} (A) - \cos^{4} (A)}{\cos (A) - \sin (A)}$
4514	Simplify	1/(csc(x-1))-1/(csc(x+1))	$\frac{1}{\csc (x - 1)} - \frac{1}{\csc (x + 1)}$
4515	Simplify	1/(sec(x)-tan(x))-1/(sec(x)+tan(x))	$\frac{1}{\sec (x) - \tan (x)} - \frac{1}{\sec (x) + \tan (x)}$
4516	Simplify	1/(cot(x)^2+1)	$\frac{1}{\cot^{2} (x) + 1}$
4517	Simplify	1/(tan(x)+cot(x))	$\frac{1}{\tan (x) + \cot (x)}$
4518	Simplify	(1+cos(x))/(sin(x))	$\frac{1 + \cos (x)}{\sin (x)}$
4519	Simplify	(1+tan(x)^2)/(1+cot(x)^2)	$\frac{1 + \tan^{2} (x)}{1 + \cot^{2} (x)}$
4520	Simplify	(1+sin(x))/(cos(x))+(cos(x))/(1+sin(x))	$\frac{1 + \sin (x)}{\cos (x)} + \frac{\cos (x)}{1 + \sin (x)}$
4521	Simplify	10^p*4	$10^{p} \cdot 4$
4522	Simplify	(11pi)/12	$\frac{11 π}{12}$
4523	Solve for ?	y=sin(x)	$y = \sin (x)$
4524	Solve for ?	tan(x/2) = square root of 3	$\tan (\frac{x}{2}) = \sqrt{3}$
4525	Solve for ?	tan(x/2-pi/4)=1	$\tan (\frac{x}{2} - \frac{π}{4}) = 1$
4526	Solve for ?	tan(x)=4/5	$\tan (x) = \frac{4}{5}$
4527	Solve for ?	tan(x)=5/12	$\tan (x) = \frac{5}{12}$
4528	Solve for ?	tan(x)=- square root of 2sin(x)	$\tan (x) = - \sqrt{2} \sin (x)$
4529	Solve for ?	tan(x)=5	$\tan (x) = 5$
4530	Solve for ?	sin(x) = square root of 3/2	$\sin (x) = \sqrt{\frac{3}{2}}$
4531	Solve for ?	sin(x)=8/17	$\sin (x) = \frac{8}{17}$
4532	Solve for ?	sin(2x)=2sin(x)cos(x)	$\sin (2 x) = 2 \sin (x) \cos (x)$
4533	Solve for ?	sin(2x)=-( square root of 2)/2	$\sin (2 x) = - \frac{\sqrt{2}}{2}$
4534	Solve for ?	sin(x/2)=( square root of 2)/2	$\sin (\frac{x}{2}) = \frac{\sqrt{2}}{2}$
4535	Solve for ?	sin(x)sec(x)cot(x)=1	$\sin (x) \sec (x) \cot (x) = 1$
4536	Solve for ?	csc(x)=- square root of 2	$\csc (x) = - \sqrt{2}$
4537	Solve for ?	sec(x/2)=cos(x/2)	$\sec (\frac{x}{2}) = \cos (\frac{x}{2})$
4538	Solve for ?	r=8cos(x)	$r = 8 \cos (x)$
4539	Solve for ?	cos(2x)=sin(x)	$\cos (2 x) = \sin (x)$
4540	Solve for ?	x=arctan(( square root of 3)/3)	$x = \arctan (\frac{\sqrt{3}}{3})$
4541	Solve for ?	tan(x)^4-20tan(x)^2+64=0	$\tan^{4} (x) - 20 \tan^{2} (x) + 64 = 0$
4542	Solve for ?	cos(x)^2(1+tan(x)^2)=1	$\cos^{2} (x) (1 + \tan^{2} (x)) = 1$
4543	Solve for ?	sec(x)^2(1-sin(x)^2)=1	$\sec^{2} (x) (1 - \sin^{2} (x)) = 1$
4544	Solve for ?	2cos(x)^2-11cos(x)+5=0	$2 \cos^{2} (x) - 11 \cos (x) + 5 = 0$
4545	Solve for ?	2cos(x)^2+ square root of 3cos(x)=0	$2 \cos^{2} (x) + \sqrt{3} \cos (x) = 0$
4546	Solve for ?	2cos(x)^2-cos(x)=0	$2 \cos^{2} (x) - \cos (x) = 0$
4547	Solve for ?	square root of 3csc(x)+2=0	$\sqrt{3} \csc (x) + 2 = 0$
4548	Solve for ?	16sin(x)^2-12=0	$16 \sin^{2} (x) - 12 = 0$
4549	Solve for ?	4sin(x)-1=2sin(x)	$4 \sin (x) - 1 = 2 \sin (x)$
4550	Solve for ?	6cos(x)^2=3	$6 \cos^{2} (x) = 3$
4551	Solve for ?	cos(x)=3/4	$\cos (x) = \frac{3}{4}$
4552	Solve for ?	cos(x)=-12/13	$\cos (x) = - \frac{12}{13}$
4553	Solve for ?	2sin(x)+ square root of 2=0	$2 \sin (x) + \sqrt{2} = 0$
4554	Solve for ?	2cos(3x)=1	$2 \cos (3 x) = 1$
4555	Solve for ?	4sin(x)^2-4sin(x)+1=0	$4 \sin^{2} (x) - 4 \sin (x) + 1 = 0$
4556	Solve for t	7cos(2t)=3	$7 \cos (2 t) = 3$
4557	Solve for x	(e^x+e^(-x))/2=15	$\frac{e^{x} + e^{- x}}{2} = 15$
4558	Solve for x	( square root of 2)/2*csc(x)-1=0	$\frac{\sqrt{2}}{2} \cdot \csc (x) - 1 = 0$
4559	Solve for x	(tan(x)-1)(cos(x)+1)=0	$(\tan (x) - 1) (\cos (x) + 1) = 0$
4560	Solve for b	tan(b)=15/9	$\tan (b) = \frac{15}{9}$
4561	Solve for f	f=9/5c+32	$f = \frac{9}{5} c + 32$
4562	Find the Exact Value	arccsc(- square root of 2)	$arccsc (- \sqrt{2})$
4563	Solve for x	tan(x)^2+sec(x)-1=0	$\tan^{2} (x) + \sec (x) - 1 = 0$
4564	Solve for x	sin(x)^2-1=0	$\sin^{2} (x) - 1 = 0$
4565	Solve for x	2cos(x)^2=1	$2 \cos^{2} (x) = 1$
4566	Solve for x	2cos(x)^2+3sin(x)-3=0	$2 \cos^{2} (x) + 3 \sin (x) - 3 = 0$
4567	Solve for x	2cos(x)^2-7cos(x)+3=0	$2 \cos^{2} (x) - 7 \cos (x) + 3 = 0$
4568	Solve for x	2cos(x-1)^2=0	$2 \cos^{2} (x - 1) = 0$
4569	Solve for x	16cos(x)^2-4=0	$16 \cos^{2} (x) - 4 = 0$
4570	Solve for x	24arcsin(x)=4pi	$24 \arcsin (x) = 4 π$
4571	Solve for x	2sin(2x)cos(x)-sin(x)=0	$2 \sin (2 x) \cos (x) - \sin (x) = 0$
4572	Solve for x	2sin(3x)-1=0	$2 \sin (3 x) - 1 = 0$
4573	Solve for x	2sin(2x)- square root of 3=0	$2 \sin (2 x) - \sqrt{3} = 0$
4574	Solve for x	2cos(2x)+1=0	$2 \cos (2 x) + 1 = 0$
4575	Solve for x	12arcsin(x)=2pi	$12 \arcsin (x) = 2 π$
4576	Solve for x	cos(x)+2sin(x)cos(x)=0	$\cos (x) + 2 \sin (x) \cos (x) = 0$
4577	Solve for x	cos(x)+sin(x)tan(x)=2	$\cos (x) + \sin (x) \tan (x) = 2$
4578	Solve for x	cos(x)=3/4	$\cos (x) = \frac{3}{4}$
4579	Solve for x	cot(x)=-1/( square root of 3)	$\cot (x) = - \frac{1}{\sqrt{3}}$
4580	Solve for x	cos(x+pi/4)-cos(x-pi/4)=1	$\cos (x + \frac{π}{4}) - \cos (x - \frac{π}{4}) = 1$
4581	Solve for x	cos(x)sin(x)-2cos(x)=0	$\cos (x) \sin (x) - 2 \cos (x) = 0$
4582	Solve for x	8cos(x)^2=4	$8 \cos^{2} (x) = 4$
4583	Solve for x	9tan(x)^2-3=0	$9 \tan^{2} (x) - 3 = 0$
4584	Solve for x	cos(2x) = square root of 2-cos(2x)	$\cos (2 x) = \sqrt{2} - \cos (2 x)$
4585	Solve for x	arccos(x-1/( square root of 2))=pi/4	$\arccos (x - \frac{1}{\sqrt{2}}) = \frac{π}{4}$
4586	Solve for x	4cos(x)^2=3	$4 \cos^{2} (x) = 3$
4587	Solve for x	4cos(4x)^2-3=0	$4 \cos^{2} (4 x) - 3 = 0$
4588	Solve for x	4cos(x)=1+2cos(x)	$4 \cos (x) = 1 + 2 \cos (x)$
4589	Solve for x	6arccos(x)=pi	$6 \arccos (x) = π$
4590	Solve for x	sin(x)cos(x)=( square root of 3)/4	$\sin (x) \cos (x) = \frac{\sqrt{3}}{4}$
4591	Solve for x	sin(x)=tan(x)	$\sin (x) = \tan (x)$
4592	Solve for x	tan(x/2)=( square root of 3)/3	$\tan (\frac{x}{2}) = \frac{\sqrt{3}}{3}$
4593	Solve for x	tan(2x)=- square root of 3	$\tan (2 x) = - \sqrt{3}$
4594	Solve for x	tan(x)=-4	$\tan (x) = - 4$
4595	Solve for x	tan(x)=3.5	$\tan (x) = 3.5$
4596	Solve for x	sec(x)- square root of 2=0	$\sec (x) - \sqrt{2} = 0$
4597	Solve for x	sin(x/2)=-( square root of 3)/2	$\sin (\frac{x}{2}) = - \frac{\sqrt{3}}{2}$
4598	Solve for x	sin(x/2)=1-sin(x/2)	$\sin (\frac{x}{2}) = 1 - \sin (\frac{x}{2})$
4599	Solve for x	csc(x)=1	$\csc (x) = 1$
4600	Solve for x	natural log of x^2-12 = natural log of x	$\ln (x^{2} - 12) = \ln (x)$