Trigonometry Examples

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

Step 1

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

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

Step 2

Apply pythagorean identity.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

$\cos (x)$

$\cos (x)$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$