Algebra Examples

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

Step 1

Start on the left side.

$\frac{\cot (θ)}{\csc (θ)}$

Step 2

Convert to sines and cosines.

Tap for more steps...

Step 2.1

Write $\cot (θ)$ in sines and cosines using the quotient identity.

$\frac{\frac{\cos (θ)}{\sin (θ)}}{\csc (θ)}$

Step 2.2

Apply the reciprocal identity to $\csc (θ)$ .

$\frac{\frac{\cos (θ)}{\sin (θ)}}{\frac{1}{\sin (θ)}}$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{\cos (θ)}{\sin (θ)} \sin (θ)$

Step 3.2

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

$\cos (θ)$

Step 4

Because the two sides have been shown to be equivalent, the equation is an identity.

$\frac{\cot (θ)}{\csc (θ)} = \cos (θ)$ is an identity