Question

For $A$ being acute if $\frac{2}{1-{\tan }^{2}A}=\cot A$ then find the value $A$.

Answer 1

Given,

$\frac{2}{1-{\tan }^{2}A}=\cot A$

$\Rightarrow \frac{2\tan A}{1-{\tan }^{2}A}=1$

$\Rightarrow \tan 2A=1$

$\Rightarrow 2A=\frac{\pi }{4}$ [ Since $A$ is acute}

$\therefore A=\frac{\pi }{8}$.