cosec 10 ° - 3 sec 10 ° is equal to

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Solution

Q.
$cosec 10 ° - \sqrt{3} \sec 10 °$ is equal to

1 $1$

2 $\frac{1}{2}$

3 $2$

4 $4$

Ans.
(4)

$cosec 10 ° - \sqrt{3} \sec 10 °$

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

$= (\frac{\cos 10 °}{2} - \frac{\sqrt{3}}{2} \sin 10 °) \frac{4}{\sin 20 °}$

$= \frac{4 \sin (30 ° - 10 °)}{\sin 20 °} = 4$

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