Trigonometry Examples

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

Start on the right side.

$\sec (x) + \tan (x)$

Convert to sines and cosines.

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

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

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

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

Combine the numerators over the common denominator.

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

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