Question

The value of the expression $\frac{(1+\cos 2A)(1-\sec 2A)}{\cot A(1+\tan A)(1-\cot A)}$, when $A={30}^{\circ }$ is

Answer 1

$y=\frac{(1+\cos 2A)(1-\sec 2A)}{\cot A(1+\tan A)(1-\cot A)}$
Putting $A={30}^{\circ }$, we get
$y=\frac{(1+\cos {60}^{\circ })(1-\sec {60}^{\circ })}{\cot {30}^{\circ }(1+\tan {30}^{\circ })(1-\cot {30}^{\circ })}=\frac{(1+\frac{1}{2})(1-2)}{\sqrt{3}(1+\frac{1}{\sqrt{3}})(1-\sqrt{3})}=\frac{-\frac{3}{2}}{-(\sqrt{3}+1)(\sqrt{3}-1)}\therefore y=\frac{3}{4}=0.75$