Determine if True csc(theta)^2-cot(theta)^2=cot(theta)tan(theta)

$\csc^{2} (θ) - \cot^{2} (θ) = \cot (θ) \tan (θ)$

Step 1

Start on the left side.

$\csc^{2} (θ) - \cot^{2} (θ)$

Step 2

Apply pythagorean identity.

$1$

Step 3

Rewrite $1$ as $\cot (θ) \tan (θ)$ .

$\cot (θ) \tan (θ)$

Step 4

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

$\csc^{2} (θ) - \cot^{2} (θ) = \cot (θ) \tan (θ)$ is an identity