Question

If $\sin \theta \sim \cos \theta =\sqrt{2}\cos ({90}^o-\theta )$, find the value of $\cot \theta$.

Answer 1

We have

$\begin{array}{c}\sin \theta -\cos \theta =\sqrt{2}\cos \left({90}^{\circ }-\theta \right)\\ \sin \theta -\cos \theta =\sqrt{2}\sin \theta \\ \sin \left(1-\sqrt{2}\right)=\cos \theta \\ \cot \theta =1-\sqrt{2}\\ hence,\\ \cot \theta =1-\sqrt{2}\end{array}$