Trigonometry Examples

$\sin^{2} (20) + \frac{1}{\sec^{2} (20)}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $1$ as $1^{2}$ .

$\sin^{2} (20) + \frac{1^{2}}{\sec^{2} (20)}$

Step 1.2

Rewrite $\frac{1^{2}}{\sec^{2} (20)}$ as ${(\frac{1}{\sec (20)})}^{2}$ .

$\sin^{2} (20) + {(\frac{1}{\sec (20)})}^{2}$

Step 1.3

Rewrite $\sec (20)$ in terms of sines and cosines.

$\sin^{2} (20) + {(\frac{1}{\frac{1}{\cos (20)}})}^{2}$

Step 1.4

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\cos (20)}$ .

$\sin^{2} (20) + {(1 \cos (20))}^{2}$

Step 1.5

Multiply $\cos (20)$ by $1$ .

$\sin^{2} (20) + \cos^{2} (20)$

Step 2

Apply pythagorean identity.

$1$