We are given the trigonometric equation:
(1 - sec x) / (1 - cos x) = - sec x
Since the left side has more terms, then let us work on
that side to make it exactly like the right side.
We know that sec = 1 / cos, therefore:
(1 – 1 / cos x) / (1 – cos x) = - sec x
[(cos x – 1) / cos x] / (1 – cos x) = - sec x
[- (1 – cos x) / cos x] / (1 – cos x) = - sec x
Cancelling out the term (1 – cos x):
- 1 / cos x = - sec x
- sec x = - sec x
PROVEN!
