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3.Trigonometrical Ratios, Functions and Identities
medium
$\frac{1}{{\sin 10^\circ }} - \frac{{\sqrt 3 }}{{\cos 10^\circ }} =$
A
$0$
B
$1$
C
$2$
D
$4$
(IIT-1974)
Solution
(d) $\frac{1}{{\sin 10^\circ }} – \frac{{\sqrt 3 }}{{\cos 10^\circ }}$
$ = \frac{{2\left( {\frac{{\cos 10^\circ }}{2} – \frac{{\sqrt 3 }}{2}\sin 10^\circ } \right)}}{{(2\sin 10^\circ \cos 10^\circ ) \times \frac{1}{2}}}$
$ = \frac{{4\,\sin \,({{30}^o} – {{10}^o})}}{{\sin \,{{20}^o}}} $
$= \frac{{4\,\sin \,{{20}^o}}}{{\sin \,{{20}^o}}} = 4$.
Standard 11
Mathematics
