Question

For $\alpha$ being acute solve:

$\cos \alpha =\cot \alpha$.

Answer 1

Given,

$\cos \alpha =\cot \alpha$

or, $\cos \alpha .\sin \alpha =\cos \alpha$

or, $\cos \alpha (\sin \alpha -1)=0$

or, $\cos \alpha =0$ and $\sin \alpha =1$

Since $\alpha$ is acute then solving both the equation we get,

$\alpha =\frac{\pi }{2}$.