Question

The value of $\sqrt{3}\csc {20}^{}-\sec {20}^{}$ is equal to

• A. $2$
• B. $2\sin {20}^{}-\csc {40}^{}$
• C. $4$
• D. $4\sin {20}^{},\csc {40}^{}$

Answer 1

The correct option is C $4$

The value of $\sqrt{3}\csc 20-\sec 20$ is equal to
$=\frac{\tan 60}{\sin 20}-\frac{1}{\cos 20}$
$=\frac{\sin 60\cos 20-\sin 20\cos 60}{\cos 60\sin 20\cos 20}$
$=\frac{\sin 40}{\cos 60\sin 20\cos 20}$
$=\frac{2\sin 20\cos 20}{\frac{1}{2}\sin 20\cos 20}$ .....[Using $\sin 2\theta =2\sin \theta .\cos \theta$]

$=4$