Trigonometry Examples

$\frac{1 - \cos (x)}{\sin (x)} = \csc (x) - \cot (x)$

Step 1

Start on the right side.

$\csc (x) - \cot (x)$

Step 2

Convert to sines and cosines.

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Step 2.1

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

$\frac{1}{\sin (x)} - \cot (x)$

Step 2.2

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

$\frac{1}{\sin (x)} - \frac{\cos (x)}{\sin (x)}$

Step 3

Combine the numerators over the common denominator.

$\frac{1 - \cos (x)}{\sin (x)}$

Step 4

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

$\frac{1 - \cos (x)}{\sin (x)} = \csc (x) - \cot (x)$ is an identity