1 10^ - 3 10^ = - Vidyadip

MCQ

$\frac{1}{{\sin 10^\circ }} - \frac{{\sqrt 3 }}{{\cos 10^\circ }} =$

A
$0$
B
$1$
C
$2$
✓
$4$

✓

Answer

Correct option: D.

$4$

d
(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}}} $

$= \frac{{4\,\sin \,{{20}^o}}}{{\sin \,{{20}^o}}} = 4$.

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