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 that $	an 	heta + \cot 	heta = 2$.We know that $	an 	heta = \frac{\sin 	heta}{\cos 	heta}$ and $\cot 	heta = \frac{\cos 	heta}{\sin

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) Given that $	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 values,we get $\frac{\sin 	heta}{\cos 	heta} + \frac{\cos 	heta}{\sin 	heta} = 2$.Taking the common denominator,$\frac{\sin^2 	heta + \cos^2 	heta}{\sin 	heta \cos 	heta} = 2$.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 $2 \sin 	heta \cos 	heta = 1$,which is $\sin 2 	heta = 1$.Thus,$2 	heta = \frac{\pi}{2}$,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

Which of the following is a primary lymphoid organ?

If $\theta$ is the angle between vectors $\vec{a}$ and $\vec{b}$ and $|\vec{a} \times \vec{b}| = |\vec{a} \cdot \vec{b}|$,then $\theta$ is equal to

The difference between volume and pressure coefficients of an ideal gas is

If a solid sphere of mass $1 \ kg$ and radius $0.1 \ m$ rolls without slipping at a uniform velocity of $1 \ m/s$ along a straight line on a horizontal floor,the kinetic energy is

Vedclass Test Series

Exam Paper Generator

Online Exam Module