Trigonometry Examples

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

Step 1

Multiply by $1$ .

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

Step 2

Simplify with factoring out.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 3

Apply pythagorean identity.

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

Step 4

Rewrite $\sec (x)$ in terms of sines and cosines.

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

Step 5

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

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Step 5.1

Factor $\cos (x)$ out of $\cos^{2} (x)$ .

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

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

$\cos (x)$