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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

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

Vedclass · Answer

(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

Similar Questions

If $\cosh 2x = 241$,then $\operatorname{coth} x$ is equal to

The value of the expression $1 - \frac{\sin^2 y}{1 + \cos y} + \frac{1 + \cos y}{\sin y} - \frac{\sin y}{1 - \cos y}$ is equal to

If $\sec \theta + \tan \theta = \frac{1}{3}$,then the quadrant in which $2 \theta$ lies is

If $\frac{2 \sin \alpha}{1+\cos \alpha+\sin \alpha}=x$,then $\frac{1-\cos \alpha-\sin \alpha}{\cos \alpha}=$

Choose the $INCORRECT$ statement$(s)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module