Question

If $\tan A=$ $\sqrt{2}$ $-1$ then $\sin A\cos A$ $=\frac{\sqrt{2}}{m}$.Find $m$

Answer 1

Given,

$\tan A=\sqrt{2}-1$

rationalizing the factor, we get,

$\tan A=\frac{1}{\sqrt{2}+1}$

$\Rightarrow \frac{1}{\tan A}=\sqrt{2}+1$

we get,

$\tan A+\frac{1}{\tan A}=\sqrt{2}-1+\sqrt{2}+1$

$\frac{{\tan }^{2}A+1}{\tan A}=2\sqrt{2}$

$\frac{1}{\sin A\cos A}=2\sqrt{2}$

$\therefore \sin A\cos A=\frac{1}{2\sqrt{2}}$

$\sin A\cos A=\frac{\sqrt{2}}{4}$

$\therefore m=4$