Question

Complete the identity. sec 0 - sece =? Any one can please help me?

Answer 1

Answer:

$\frac{\sin^2(\theta)}{\cos(\theta)}$

Step-by-step explanation:

$\sec(\theta)-\frac{1}{\sec(\theta)}$

Write first term as a fraction:

$\frac{\sec(\theta)}{1}-\frac{1}{\sec(\theta)}$

Multiply first fraction by $1=\frac{\sec(\theta)}{\sec(\theta)}$:

$\frac{\sec^2(\theta)-1}{\sec(\theta)}$

Use Pythagoren Identity, $\tan^2(\theta)+1=\sec^2(\theta)$:

$\frac{\tan^2(\theta)}{\sec(\theta)}$

Rewrite using quotient identity, $\frac{\sin(\theta)}{\cos(\theta)}=\tan(\theta)$, and recirpocal identity, $\frac{1}{\cos(\theta)}=\sec(\theta)$:

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

A factor of $\frac{1}{\cos(\theta)}$ cancels:

$\frac{\sin^2(\theta)}{\cos(\theta)}$