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Trigonometry Examples

({cos}^{2} (x)) (1 + {tan}^{2} (x))

$(\cos^{2} (x)) (1 + \tan^{2} (x))$

Step 1

Rearrange terms.

{cos}^{2} (x) ({tan}^{2} (x) + 1)

$\cos^{2} (x) (\tan^{2} (x) + 1)$

Step 2

Apply pythagorean identity.

{cos}^{2} (x) {sec}^{2} (x)

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

Step 3

Rewrite

sec (x)

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

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

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

Step 4

Simplify the expression.

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Step 4.1

Apply the product rule to

\frac{1}{cos (x)}

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

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

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

Step 4.2

One to any power is one.

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

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

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

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

Step 5

Cancel the common factor of

{cos}^{2} (x)

$\cos^{2} (x)$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

$1$

$1$

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