Trigonometry Examples

$\sec (θ) \cos (θ) + \sec (θ) \sin (θ) = 1 + \tan (θ)$

Step 1

Start on the left side.

$\sec (θ) \cos (θ) + \sec (θ) \sin (θ)$

Step 2

Convert to sines and cosines.

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Step 2.1

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

$\frac{1}{\cos (θ)} \cos (θ) + \sec (θ) \sin (θ)$

Step 2.2

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

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

Step 3

Simplify each term.

$1 + \frac{\sin (θ)}{\cos (θ)}$

Step 4

Rewrite $1 + \frac{\sin (θ)}{\cos (θ)}$ as $1 + \tan (θ)$ .

$1 + \tan (θ)$

Step 5

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

$\sec (θ) \cos (θ) + \sec (θ) \sin (θ) = 1 + \tan (θ)$ is an identity