Question

HELP!!! ASAP!!!! TRIG!!!

Answer 1

Identity is true

Explanation:

`(cos\theta+1)/(tan^2\theta)=(cos\theta)/(sec\theta-1)`

`(cos\theta+1)(sec\theta-1)=(tan^2\theta)(cos\theta)`

`(cos\theta)(sec\theta)+(cos\theta)(-1)+(1)(sec\theta)+(1)(-1)=((sin^2\theta)/(cos^2\theta))(cos\theta)`

`(cos\theta)((1)/(cos\theta))-cos\theta+sec\theta-1=(sin^2\theta)/(cos\theta)`

`1-cos\theta+sec\theta-1=(sin^2\theta)/(cos\theta)`

`-cos\theta+sec\theta=(sin^2\theta)/(cos\theta)`

`sec\theta-cos\theta=(sin^2\theta)/(cos\theta)`

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

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

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

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

Therefore, the identity is true.

Helpful tips:

Pythagorean Identity:
`sin^2\theta+cos^2\theta=1\\cos^2\theta=1-sin^2\theta\\sin^2\theta=1-cos^2\theta`

Quotient Identities:
`tan\theta=(sin\theta)/(cos\theta),sec\theta=(1)/(cos\theta)`