Question

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

Answer 1

We have

$\sin x-\cos x=\sqrt{2}\cos (90-x)=\sqrt{2}\sin x$

$\cos x=\sin x-\sqrt{2}\sin x$

$\cos x=\sin x(1-\sqrt{2})$

To obtain $\cot x$, divide it throughout $\sin x$,

$\cot x=1-\sqrt{2}$

Hence, this is the answer.