Precalculus Examples

$\sin^{2} (θ) \csc^{2} (θ) = \sin^{2} (θ) + \cos^{2} (θ)$

Step 1

Start on the right side.

$\sin^{2} (θ) + \cos^{2} (θ)$

Step 2

Apply pythagorean identity.

$1$

Step 3

Rewrite $1$ as $\sin^{2} (θ) \csc^{2} (θ)$ .

$\sin^{2} (θ) \csc^{2} (θ)$

Step 4

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

$\sin^{2} (θ) \csc^{2} (θ) = \sin^{2} (θ) + \cos^{2} (θ)$ is an identity