Question

$\sqrt{3}cosec{20}^{\circ }-\sec {20}^{\circ }$ is equal to :

• A. $2$
• B. $2\sin {20}^{\circ }/\sin {40}^{\circ }$
• C. $4$
• D. $4\sin {20}^{\circ }/\sin {40}^{\circ }$

Answer 1

The correct option is C $4$

Given expression is $\frac{\sqrt{3}}{sin20}-\frac{1}{cos20}$

$=2(\frac{\frac{\sqrt{3}}{2}}{sin20}-\frac{\frac{1}{2}}{cos20})$

$=2(\frac{sin60}{sin20}-\frac{cos60}{cos20})$

$=2\left(\frac{sin60cos20-cos60sin20}{sin20cos20}\right)$

$=2\left(\frac{sin(60-20)}{sin20cos20}\right)$

$=2\frac{sin40}{sin20cos20}$

$=2\times \frac{2sin20cos20}{sin20cos20}=4$