Q:

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

Accepted Solution

A:
Answer:[tex]\frac{\sin^2(\theta)}{\cos(\theta)}[/tex]Step-by-step explanation:[tex]\sec(\theta)-\frac{1}{\sec(\theta)}[/tex]Write first term as a fraction:[tex]\frac{\sec(\theta)}{1}-\frac{1}{\sec(\theta)}[/tex]Multiply first fraction by [tex]1=\frac{\sec(\theta)}{\sec(\theta)}[/tex]:[tex]\frac{\sec^2(\theta)-1}{\sec(\theta)}[/tex]Use Pythagoren Identity, [tex]\tan^2(\theta)+1=\sec^2(\theta)[/tex]:[tex]\frac{\tan^2(\theta)}{\sec(\theta)}[/tex]Rewrite using quotient identity, [tex]\frac{\sin(\theta)}{\cos(\theta)}=\tan(\theta)[/tex], and recirpocal identity, [tex]\frac{1}{\cos(\theta)}=\sec(\theta)[/tex]:[tex]\frac{\frac{\sin^2(\theta)}{\cos^2(\theta)}}{\frac{1}{\cos(\theta)}}[/tex]A factor of [tex]\frac{1}{\cos(\theta)}[/tex] cancels:[tex]\frac{\sin^2(\theta)}{\cos(\theta)}[/tex]