Question

If $cosecA=\sqrt{2}$, find the value of $\frac{2{\sin }^{2}A+3{\cot }^{2}A}{4({\tan }^{2}A-{\cos }^{2}A)}$

Answer 1

Given : $cosecA=\sqrt{2}$

$\therefore A=\frac{\pi }{4}={45}^0$

$\sin A=sin{45}^0=\frac{1}{\sqrt{2}}$

$\cot A=cot{45}^0=1,$

$\tan A=tan{45}^0=1$

$\cos A=cot{45}^0=\frac{1}{\sqrt{2}}$

$\therefore \frac{2{\sin }^{2}A+3{\cot }^{2}A}{4({\tan }^{2}A-{\cos }^{2}A)}=\frac{2\left(\frac{1}{2}\right)+3\left(1\right)}{4(1-\left(\frac{1}{2}\right))}=2$