Question

If $\sin A+\cos A=\sqrt{2}\sin (90-A)$, then find $\cot A$.

Answer 1

Given equation is written as $sinA+cosA=\sqrt{2}cosA$

$sinA=cosA(\sqrt{2}-1)$

$cotA=\frac{cosA}{sinA}=\frac{1}{\sqrt{2}-1}$

$cotA=\sqrt{2}+1$