Question #422ca

2 Answers
Feb 23, 2017

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

Feb 23, 2017

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.