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