Question

Find the value of $\frac{cosec{60}^o+sec{60}^o+cosec{45}^o}{sec{45}^o+cosec{60}^o+sec{30}^o}$

• A.
• B.
• C.
• D.

Answer 1

The correct option is D ($\frac{2+2\sqrt{3}+\sqrt{6}}{\sqrt{6}+4}$)

$\frac{cosec{60}^o+sec{60}^o+cosec{45}^o}{sec{45}^o+cosec{60}^o+sec{30}^o}$

$=\frac{\frac{2}{\sqrt{3}}+2+\sqrt{2}}{\sqrt{2}+\frac{2}{\sqrt{3}}+\frac{2}{\sqrt{3}}}$

$=\frac{2+2\sqrt{3}+\sqrt{6}}{\sqrt{6}+2+2}$

$=\frac{2+2\sqrt{3}+\sqrt{6}}{\sqrt{6}+4}$