Question

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

Answer 1

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

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