1 - + 1 - = - Vidyadip

MCQ

$\frac{{\sin \theta }}{{1 - \cot \theta }} + \frac{{\cos \theta }}{{1 - \tan \theta }} = $

A
$0$
B
$1$
C
$\cos \theta - \sin \theta $
✓
$\cos \theta + \sin \theta $

✓

Answer

Correct option: D.

$\cos \theta + \sin \theta $

d
(d) $\frac{{\sin \theta }}{{1 - \cot \theta }} + \frac{{\cos \theta }}{{1 - \tan \theta }}$

$ = \frac{{\sin \theta \,.\,\sin \theta }}{{\,\sin \theta - \cos \theta }} + \frac{{\cos \theta \,.\cos \theta }}{{\cos \theta - \sin \theta }}$

$ = \frac{{({{\cos }^2}\theta - {{\sin }^2}\theta )}}{{(\cos \theta - \sin \theta )}} = \cos \theta + \sin \theta $.

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