Question

If $co\sec A=2$, find the value of $\frac{1}{\tan A}+\frac{\sin A}{1+\cos A}$

Answer 1

$cosecA=2$

$sinA=\frac{1}{2}$

$A={30}^o$

Therefore,

$\frac{1}{tanA}+\frac{sinA}{1+cosA}$=$\frac{1}{tan{30}^o}+\frac{sin{30}^o}{1+cos{30}^o}$

$=\sqrt{3}+\frac{\frac{1}{2}}{1+\frac{\sqrt{3}}{2}}$

$=\sqrt{3}+\frac{1}{2+\sqrt{3}}$

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

On Rationalisation,

$=4\sqrt{3}+8-6-4\sqrt{3}$

$=2$