Trigonometry Examples

$(5 \sec^{2} (x)) (1 - \sin^{2} (x))$

Step 1

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

$5 {(\frac{1}{\cos (x)})}^{2} (1 - \sin^{2} (x))$

Step 2

Combine fractions.

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Step 2.1

Apply the product rule to $\frac{1}{\cos (x)}$ .

$5 \frac{1^{2}}{\cos^{2} (x)} (1 - \sin^{2} (x))$

Step 2.2

One to any power is one.

$5 \frac{1}{\cos^{2} (x)} (1 - \sin^{2} (x))$

Step 2.3

Combine $5$ and $\frac{1}{\cos^{2} (x)}$ .

$\frac{5}{\cos^{2} (x)} (1 - \sin^{2} (x))$

$\frac{5}{\cos^{2} (x)} (1 - \sin^{2} (x))$

Step 3

Apply pythagorean identity.

$\frac{5}{\cos^{2} (x)} \cos^{2} (x)$

Step 4

Cancel the common factor of $\cos^{2} (x)$ .

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Step 4.1

Cancel the common factor.

$\frac{5}{\cos^{2} (x)} \cos^{2} (x)$

Step 4.2

Rewrite the expression.

$5$

$5$

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