Trigonometry Examples

$\sin (x) \cdot \csc (x) = 1$

Step 1

Start on the left side.

$\sin (x) \cdot \csc (x)$

Step 2

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

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

Step 3

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

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Cancel the common factor.

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

Rewrite the expression.

$1$

Step 4

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

$\sin (x) \cdot \csc (x) = 1$ is an identity