If tan theta + cot theta = 2,then sin theta i | vedclass

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(A) Given,$	an 	heta + \cot 	heta = 2$.We know that $	an 	heta = \frac{\sin 	heta}{\cos 	heta}$ and $\cot 	heta = \frac{\cos 	heta}{\sin 	he

Vedclass · Accepted Answer

$\frac{1}{\sqrt{2}}$

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(A) Given,$	an 	heta + \cot 	heta = 2$.We know that $	an 	heta = \frac{\sin 	heta}{\cos 	heta}$ and $\cot 	heta = \frac{\cos 	heta}{\sin 	heta}$.Substituting these,we get $\frac{\sin 	heta}{\cos 	heta} + \frac{\cos 	heta}{\sin 	heta} = 2$.Taking the $LCM$,$\frac{\sin^2 	heta + \cos^2 	heta}{\sin 	heta \cos 	heta} = 2$.Since $\sin^2 	heta + \cos^2 	heta = 1$,we have $\frac{1}{\sin 	heta \cos 	heta} = 2$,which implies $\sin 	heta \cos 	heta = \frac{1}{2}$.Multiplying both sides by $2$,we get $2 \sin 	heta \cos 	heta = 1$,so $\sin 2 	heta = 1$.This means $2 	heta = \frac{\pi}{2}$,so $	heta = \frac{\pi}{4}$.Therefore,$\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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