Trigonometry Examples

$\sec (x) - \sec (x) \sin^{2} (x) = \cos (x)$

Step 1

Start on the left side.

$\sec (x) - \sec (x) \sin^{2} (x)$

Step 2

Apply Pythagorean identity.

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Step 2.1

Multiply by $1$ .

$\sec (x) \cdot 1 - \sec (x) \sin^{2} (x)$

Step 2.2

Factor $\sec (x)$ out of $- \sec (x) \sin^{2} (x)$ .

$\sec (x) \cdot 1 + \sec (x) (- 1 \sin^{2} (x))$

Step 2.3

Factor $\sec (x)$ out of $\sec (x) \cdot 1 + \sec (x) (- 1 \sin^{2} (x))$ .

$\sec (x) \cdot (1 - 1 \sin^{2} (x))$

Step 2.4

Rewrite $- 1 \sin^{2} (x)$ as $- \sin^{2} (x)$ .

$\sec (x) \cdot (1 - \sin^{2} (x))$

Step 2.5

Apply pythagorean identity.

$\sec (x) \cdot \cos^{2} (x)$

Step 3

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

$\frac{1}{\cos (x)} \cdot \cos^{2} (x)$

Step 4

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

$\cos (x)$

Step 5

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

$\sec (x) - \sec (x) \sin^{2} (x) = \cos (x)$ is an identity