Trigonometry Examples

$\frac{\cot (x)}{\csc (x)} = \cos (x)$

Step 1

Simplify $\frac{\cot (x)}{\csc (x)}$ .

Tap for more steps...

Step 1.1

Rewrite $\csc (x)$ in terms of sines and cosines.

$\frac{\cot (x)}{\frac{1}{\sin (x)}} = \cos (x)$

Step 1.2

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

$\frac{\frac{\cos (x)}{\sin (x)}}{\frac{1}{\sin (x)}} = \cos (x)$

Step 1.3

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

$\frac{\cos (x)}{\sin (x)} \sin (x) = \cos (x)$

Step 1.4

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

$\frac{\cos (x)}{\sin (x)} \cdot \frac{\sin (x)}{1} = \cos (x)$

Step 1.5

Cancel the common factor of $\sin (x)$ .

Tap for more steps...

Step 1.5.1

Cancel the common factor.

$\frac{\cos (x)}{\sin (x)} \cdot \frac{\sin (x)}{1} = \cos (x)$

Step 1.5.2

Rewrite the expression.

$\cos (x) = \cos (x)$

Step 2

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

$x \approx 0, - 0.1, 0.1, - \frac{1}{5}, \frac{1}{5}, - 0.3, - \frac{2}{5}$

Step 3