Answer
Showed that given statement, $ \sin\theta( \sec\theta + \csc\theta) $ = $\tan\theta + 1$,
is an identity as left side transforms into right side.
Work Step by Step
Given statement is-
$ \sin\theta( \sec\theta + \csc\theta) $ = $\tan\theta + 1$
Left Side = $ \sin\theta$ $( \sec\theta + \csc\theta) $
= $ \sin\theta $ $( \frac{1}{\cos\theta} +\frac{1}{\sin\theta}) $
= $ \frac{\sin\theta}{\cos\theta} +\frac{\sin\theta}{\sin\theta} $
= $ \tan\theta$ + 1
= Right Side
i.e. Left Side transforms into Right Side
i.e. Given statement,$ \sin\theta( \sec\theta + \csc\theta) $ = $\tan\theta + 1$,
is an identity.
