If $ an heta+\cot heta=2$, then $\sin heta$ is equal to

Question

If $	an 	heta+\cot 	heta=2$, then $\sin 	heta$ is equal to

Aicharya · Accepted Answer

We have, $\begin{array}{rlrl} & & 	an 	heta+\cot 	heta & =2 \ \Rightarrow & & \frac{\sin 	heta}{\cos 	heta}+\frac{\cos 	heta}{\sin 	heta} & =2 \ \Rightarrow & \frac{\sin ^2 	heta+\cos ^2 	heta}{\sin 	heta \cos 	heta} & =2 \ \Rightarrow & 1=2 \sin 	heta \cos 	heta & \Rightarrow \sin 2 	heta=1 \ \Rightarrow & 2 	heta & =\frac{\pi}{2} \Rightarrow 	heta=\frac{\pi}{4}\end{array}$ Thus, $\quad \sin 	heta=\sin \frac{\pi}{4}=\frac{1}{\sqrt{2}}$

If $\tan \theta+\cot \theta=2$, then $\sin \theta$ is equal to

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