Trigonometry Examples

\frac{1}{\tan^{2} (x) + 1}

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

Step 1

Apply pythagorean identity.

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

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

Step 2

Simplify with factoring out.

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Step 2.1

Rewrite

1

$1$ as

1^{2}

$1^{2}$ .

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

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

Step 2.2

Rewrite

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

$\frac{1^{2}}{\sec^{2} (x)}$ as

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

${(\frac{1}{\sec (x)})}^{2}$ .

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

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

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

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

Step 3

Rewrite

\sec (x)

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

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

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

Step 4

Multiply by the reciprocal of the fraction to divide by

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

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

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

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

Step 5

Multiply

\cos (x)

$\cos (x)$ by

1

$1$ .

\cos^{2} (x)

$\cos^{2} (x)$

\frac{1}{\tan^{2} (x) + 1}

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

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