Question

Tantetha+1/tantetha =2 then find tan2tetha+1/tan2tetha

Answer 1

$\huge{\mathcal{\blue{\underline{Answer}}}}$

☑ Squaring both sides :

$( \tan( \alpha ) + \frac{1}{ \tan( \alpha ) } ) {}^{2} = (2) {}^{2} \\ \tan {}^{2} ( \alpha ) + \frac{1}{ \tan {}^{2} ( \alpha ) } + 2( \tan( \alpha ) )( \frac{1}{ \tan( \alpha ) }) = 4 \\ \tan {}^{2} ( \alpha ) + \frac{1}{ \tan {}^{2} ( \alpha ) } + 2 = 4 \\ \tan {}^{2} ( \alpha ) + \frac{1}{ \tan {}^{2} ( \alpha ) } = 4 - 2 \\ \tan {}^{2} ( \alpha ) + \frac{1}{ \tan {}^{2} ( \alpha ) } = 2$