Question

The value of $co\sec {10}^{\circ }-\sqrt{}3\sec {10}^{\circ }$ is equal to

• A. $\frac{1}{2}$
• B. 2
• C. 4
• D. 8

Answer 1

The correct option is C 4

$a=\csc 10-\sqrt{3}sec10$
$\Rightarrow a=\frac{\cos 10-\sqrt{3}\sin 10}{\sin 10\cos 10}=\frac{4(\sin 30\cos 10-\cos 30\sin 10)}{2\sin 10\cos 10}$
$\Rightarrow a=\frac{4\sin 20}{\sin 20}=4\{\because 2\sin A\cos A=\sin 2A\&\sin A\cos B-\cos A\sin B=\sin (A-B)\}$
Ans: C