Find cos x if sin^2 x-1/ cos x=-1

Question

This is a sum and difference identity problem. I have no idea how to do this. Please give me the answer in fraction format.

Answer 1

(sin^2x-1)/cosx=-1

sin^2x+cos^2x=1 is a trig identity

from this you get sin^2x-1=-cos^2x

substitute

-cos^2x/cosx=-1

simplifying...

-cosx=-1

cosx=1