Question

If $\tan \theta +\frac{1}{\tan \theta }=2$, find the value of ${\cot }^2\theta +\frac{1}{{\cot }^2\theta }$.

Answer 1

$\tan \theta +\frac{1}{\tan \theta }=2$

$\frac{1}{\cot \theta }+\cot \theta =2$

${(\cot \theta +\frac{1}{\cot \theta })}^2=2^2$

${\cot }^2\theta +\frac{1}{{\cot }^2\theta }+2=4$

${\cot }^2\theta +\frac{1}{{\cot }^2\theta }=2$