Question

Find the value of $\frac{\cos {30}^o\tan {60}^o+\sin {60}^o\cos {60}^o}{cosec{30}^o\sec {60}^o-cosec{60}^o\cot {30}^o}$

Answer 1

$\frac{\cos {30}^0\tan {60}^0+\sin {60}^0\cos {60}^0}{cosec{30}^0\sec {60}^0-coses{60}^0\cot {30}^0}$

Putting standard trigonometric values, we get

$=\frac{\sqrt{3}/2}{2}=\frac{\sqrt{3}+\sqrt{3}/21/2}{2-2/\sqrt{3}\sqrt{3}}$

$=\frac{3/2+\sqrt{3}/4}{4-2}$

$=\frac{6+\sqrt{3}}{4.2}=\frac{6+\sqrt{3}}{8}$

$\therefore \frac{\cos {30}^0\tan {60}^0+\sin {60}^0\cos {60}^0}{cosec{30}^0\sec {60}^0-cosec{60}^0\cot {30}^0}=\frac{6+\sqrt{3}}{8}$