Question

If $sin\left(\frac{\pi cot\theta }{4}\right)=cos\left(\frac{\pi cot\theta }{4}\right)$ and $\theta$ is in the first quadrant, then $\theta$ =

• A. $\pi /3$
• B. $\pi /2$
• C. $\pi /4$
• D. None of these.

Answer 1

The correct option is C $\pi /4$

Given,

$\sin \left(\frac{\pi \cot \theta }{4}\right)=\cos \left(\frac{\pi \cot \theta }{4}\right)$

$\Rightarrow \sin \left(\frac{\pi \cot \theta }{4}\right)=\sin (\frac{\pi }{2}-\frac{\pi \cot \theta }{4})$

$\Rightarrow \frac{\pi \cot \theta }{4}=\frac{\pi }{2}-\frac{\pi \cot \theta }{4}$

$\Rightarrow 2\frac{\pi \cot \theta }{4}=\frac{\pi }{2}$

$\cot \theta =1$

$\theta ={\cot }^{-1}\left(1\right)=\frac{\pi }{4}$