Trigonometry Examples

$\frac{\csc (t + 1)}{\cot (t)} = \frac{\cot (t)}{\csc (t - 1)}$

Step 1

Simplify $\frac{\csc (t + 1)}{\cot (t)}$ .

Tap for more steps...

Step 1.1

Rewrite $\cot (t)$ in terms of sines and cosines.

$\frac{\csc (t + 1)}{\frac{\cos (t)}{\sin (t)}} = \frac{\cot (t)}{\csc (t - 1)}$

Step 1.2

Rewrite $\csc (t + 1)$ in terms of sines and cosines.

$\frac{\frac{1}{\sin (t + 1)}}{\frac{\cos (t)}{\sin (t)}} = \frac{\cot (t)}{\csc (t - 1)}$

Step 1.3

Multiply by the reciprocal of the fraction to divide by $\frac{\cos (t)}{\sin (t)}$ .

$\frac{1}{\sin (t + 1)} \cdot \frac{\sin (t)}{\cos (t)} = \frac{\cot (t)}{\csc (t - 1)}$

Step 1.4

Simplify.

Tap for more steps...

Step 1.4.1

Convert from $\frac{1}{\sin (t + 1)}$ to $\csc (t + 1)$ .

$\csc (t + 1) \frac{\sin (t)}{\cos (t)} = \frac{\cot (t)}{\csc (t - 1)}$

Step 1.4.2

Convert from $\frac{\sin (t)}{\cos (t)}$ to $\tan (t)$ .

$\csc (t + 1) \tan (t) = \frac{\cot (t)}{\csc (t - 1)}$

Step 2

Simplify $\frac{\cot (t)}{\csc (t - 1)}$ .

Tap for more steps...

Step 2.1

Rewrite $\csc (t - 1)$ in terms of sines and cosines.

$\csc (t + 1) \tan (t) = \frac{\cot (t)}{\frac{1}{\sin (t - 1)}}$

Step 2.2

Rewrite $\cot (t)$ in terms of sines and cosines.

$\csc (t + 1) \tan (t) = \frac{\frac{\cos (t)}{\sin (t)}}{\frac{1}{\sin (t - 1)}}$

Step 2.3

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\sin (t - 1)}$ .

$\csc (t + 1) \tan (t) = \frac{\cos (t)}{\sin (t)} \sin (t - 1)$

Step 2.4

Write $\sin (t - 1)$ as a fraction with denominator $1$ .

$\csc (t + 1) \tan (t) = \frac{\cos (t)}{\sin (t)} \cdot \frac{\sin (t - 1)}{1}$

Step 2.5

Simplify.

Tap for more steps...

Step 2.5.1

Divide $\sin (t - 1)$ by $1$ .

$\csc (t + 1) \tan (t) = \frac{\cos (t)}{\sin (t)} \sin (t - 1)$

Step 2.5.2

Convert from $\frac{\cos (t)}{\sin (t)}$ to $\cot (t)$ .

$\csc (t + 1) \tan (t) = \cot (t) \sin (t - 1)$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

No solution

Step 4