How to prove (1-secx) / (1-cosx) = - secx

Question

Jessie Foster

Mathematics

20 March, 05:35

How to prove (1-secx) / (1-cosx) = - secx

+2

Answers (2)

Know the Answer?

Blake Martin · Answer 1

Hello,

We suppose x ≠+/-π/2. (division by 0)

sec x=1/cos x

1-sec x = 1-1*cos x = (cos x - 1) / cos x

(1-sec x) / (1-cos x) = (cos x - 1) / (cos x * (1-cos x)) = - 1/cos x = - sec x

Daniella Morrow · Answer 2

To answer, we have to simplify the expression given. We know that:

sec x=1/cos x

1-sec x = 1-1/cos x = (cos x - 1) / cos x

(1-sec x) / (1-cos x) = (cos x - 1) / (cos x * (1-cos x)) = - 1/cos x = - sec x