Answer
As left side transforms into right side, hence given identity-
$ \frac{\sec t - \cos t}{\sec t}$ = $ \sin ^{2} t$ is verified as true.
Work Step by Step
Given identity is-
$ \frac{\sec t - \cos t}{\sec t}$ = $ \sin ^{2} t$
Taking L.S.
$ \frac{\sec t - \cos t}{\sec t}$
= $ \frac{\sec t }{\sec t} - \frac{\cos t}{\sec t} $
= $ 1 - \frac{\cos t}{1/\cos t} $
= $ 1 - \cos ^{2} t $
= $ \sin ^{2} t$
(Recall first Pythagorean identity)
= R.S.
As left side transforms into right side, hence given identity-
$ \frac{\sec t - \cos t}{\sec t}$ = $ \sin ^{2} t$ is verified as true.
