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 the sides of a right-angled triangle are ${\cos2\alpha + \cos2\beta + 2\cos(\alpha + \beta )}$ and ${\sin2\alpha + \sin2\beta + 2\sin(\alpha + \beta )}$,then the length of the hypotenuse is:

$\sin ^4 \frac{\pi}{8}+\cos ^4 \frac{\pi}{8}+\sin ^4 \frac{3 \pi}{8}+\cos ^4 \frac{3 \pi}{8}+\sin ^4 \frac{5 \pi}{8}+\cos ^4 \frac{5 \pi}{8}+\sin ^4 \frac{7 \pi}{8}+\cos ^4 \frac{7 \pi}{8}=$

If $f(x) = \frac{\cos^2 x + \sin^4 x}{\sin^2 x + \cos^4 x}$ for all $x \in R$,then $f(2023) = $

If $\tan \beta = \frac{\tan \alpha + \tan \gamma}{1 + \tan \alpha \tan \gamma}$,then $\frac{\sin 2 \alpha + \sin 2 \gamma}{1 + \sin 2 \alpha \sin 2 \gamma} = $

Let $f_k(x) = \frac{1}{k}(\cos^k x + \sin^k x)$ where $k \in \mathbb{N}$. Find the value of $f_6(x) - f_4(x)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module