Question

Question #422ca

Answer 1

Factor the numerator. Use `tan^2x+1 = sec^2x` in the denominator. Finish by simplifying the quotient.

Answer 2

See full proof below

Explanation:

I will assume you are trying to prove:

`(1-2secx-3sec^2x)/(-tan^2x)-=(1-3secx)/(1-secx)`

When proving trigonometric identities, it is sometimes wiser to start from the right-hand side and prove the left.

`(1-3secx)/(1-secx)=((1-3secx)(1+secx))/((1-secx)(1+secx))=`

`(1-3secx+secx-3sec^2x)/(1-sec^2x)=`

`(1-2secx-3sec^2x)/(-tan^2x)=`

`(3sec^2x+2secx-1)/(tan^2x)`

The final step is not needed, but adding it makes the whole expression look neater and removes the negatives.