Question

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

Answer 1

`(\sin^2(\theta))/(\cos(\theta))`

Explanation:

`\sec(\theta)-(1)/(\sec(\theta))`

Write first term as a fraction:

`(\sec(\theta))/(1)-(1)/(\sec(\theta))`

Multiply first fraction by
`1=(\sec(\theta))/(\sec(\theta))`:

`(\sec^2(\theta)-1)/(\sec(\theta))`

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

`(\tan^2(\theta))/(\sec(\theta))`

Rewrite using quotient identity,
`(\sin(\theta))/(\cos(\theta))=\tan(\theta)`, and recirpocal identity,
`(1)/(\cos(\theta))=\sec(\theta)`:

`((\sin^2(\theta))/(\cos^2(\theta)))/((1)/(\cos(\theta)))`

A factor of
`(1)/(\cos(\theta))` cancels:

`(\sin^2(\theta))/(\cos(\theta))`