Question

If $\theta$ being acute and $\cos \theta =\cot \theta$ with $\theta \ne 0$, then find the value of $\theta$.

Answer 1

Given,$\cos \theta =\cot \theta$

or, $\cos \theta =\frac{\cos \theta }{\sin \theta }$

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

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

or, $\cos \theta =0$ or $\sin \theta =1$

or, $\theta =\frac{\pi }{2}$ [ Solving both of the equation] [ As $\theta$ given to be acute]