Question

The value of the expression $\sqrt{3} cosec 20^\circ -sec 20^\circ $is equal to

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

Answer 1

Answer: (C)

$\sqrt{3} csoec 20^\circ -sec20^\circ$
$=tan 60^\circ cosec20^\circ -sec20^\circ$
$=\frac{sin60^\circ cos20^\circ-cos60^\circ. sin20^\circ}{cos60^\circ.sin20^\circ.cos20^\circ}$
$=\frac{sin(60^\circ-20^\circ)}{cos60^\circ.sin20^\circ}=\frac{sin40^\circ}{\frac{1}{4}.sin20^\circ cos20^\circ}$
$=\frac{2sin20^\circ cos20^\circ}{\frac{1}{2} sin 20^\circ cos 20^\circ}=4$