Question

Find the value of $\text{cosec}{15}^0+\sec {15}^0$.

• A. $2\sqrt{2}$
• B. $\sqrt{6}$
• C. $2\sqrt{6}$
• D. $\sqrt{6}+\sqrt{2}$

Answer 1

The correct option is C $2\sqrt{6}$

$S=\text{cosec}{15}^o+\sec {15}^o=\frac{2(\sin {15}^o+\cos {15}^o)}{2\cos {15}^o\sin {15}^o}$
Now,
$2\sin 15\cos 15=sin30=\frac{1}{2}$
$(\sin 15+\cos 15{)}^2=1+\sin 30=\frac{3}{2}$
$\Rightarrow (\sin 15+\cos 15)=\sqrt{\frac{3}{2}}$
$S=4\times \sqrt{\frac{3}{2}}=2\sqrt{6}$