Answer
Showed that given statement, $ 1 $ - $ \frac{\sin\theta}{\csc\theta}$ = $\cos^{2}\theta$,
is an identity as left side transforms into right side.
Work Step by Step
Given statement is-
$ 1 $ - $ \frac{\sin\theta}{\csc\theta}$ = $\cos^{2}\theta$
Left Side = $ 1 $ - $ \frac{\sin\theta}{\csc\theta}$
= $ 1 - \frac{\sin\theta}{1/\sin\theta}$
= $ 1$ - $ \sin\theta \times \frac{\sin\theta}{1}$
= $1$ - $\sin^{2}\theta$
= $\cos^{2}\theta$
[ From first Pythagorean identity]
= Right Side
i.e. Left Side transforms into Right Side
i.e. Given statement, $ 1 $ - $ \frac{\sin\theta}{\csc\theta}$ = $\cos^{2}\theta$,
is an identity.
