If $\sin{\left( \frac{\pi}{4}\cot heta ight) = \cos\left( \frac{\pi}{4} an heta ight)}$, then $ heta$ is equal to

Question

If $\sin{\left( \frac{\pi}{4}\cot	heta ight) = \cos\left( \frac{\pi}{4}	an	heta ight)}$, then $	heta$ is equal to

Dr. Abubacker · Accepted Answer

(d)
Given, $\sin{\left( \frac{\pi}{4}\cot	heta ight) = \cos\left( \frac{\pi}{4}	an	heta ight)}$
$\Rightarrow \ \sin{\left( \frac{\pi}{4}\cot	heta ight) = \sin\left( \frac{\pi}{2} - \frac{\pi}{4}	an	heta ight)}$
$\Rightarrow \frac{\pi}{4}\left( 	an	heta + \cot	heta ight) = \frac{\pi}{2}$
$\Rightarrow \left( 	an	heta - 1 ight)^{2} = 0\ \ \  \Rightarrow \ \ 	an	heta = 1 = 	an\frac{\pi}{4}$
$	herefore\ \ \ 	heta = n\pi + \frac{\pi}{4}$

Q. If $\sin{\left( \frac{\pi}{4}\cot\theta \right) = \cos\left( \frac{\pi}{4}\tan\theta \right)}$, then $\theta$ is equal to

Explanation

Reviewed by Dr. Abubacker

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