Trigonometry Examples

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

Step 1

Start on the right side.

$\sec (x) - \tan (x)$

Step 2

Convert to sines and cosines.

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Step 2.1

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

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

Step 2.2

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

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

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

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