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3.Trigonometrical Ratios, Functions and Identities
easy
$\frac{{\sin \theta }}{{1 - \cot \theta }} + \frac{{\cos \theta }}{{1 - \tan \theta }} = $
A
$0$
B
$1$
C
$\cos \theta - \sin \theta $
D
$\cos \theta + \sin \theta $
Solution
(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 $.
Standard 11
Mathematics
