Trigonometry Examples

$\sin (θ) \csc (θ) = \cos (θ) \sec (θ)$

Step 1

Start on the left side.

$\sin (θ) \csc (θ)$

Step 2

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

$\sin (θ) \frac{1}{\sin (θ)}$

Step 3

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

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Step 3.1

Cancel the common factor.

$\sin (θ) \frac{1}{\sin (θ)}$

Step 3.2

Rewrite the expression.

$1$

Step 4

Rewrite $1$ as $\cos (θ) \sec (θ)$ .

$\cos (θ) \sec (θ)$

Step 5

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

$\sin (θ) \csc (θ) = \cos (θ) \sec (θ)$ is an identity