If sin ^{2} alpha+sin ^{2} beta=2, then the v | vedclass

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

Question

(C) Given that $\sin ^{2} \alpha+\sin ^{2} \beta=2$.Since the maximum value of $\sin ^{2} 	heta$ is $1$,the equation $\sin ^{2} \alpha+\sin ^{2} \bet

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(C) Given that $\sin ^{2} \alpha+\sin ^{2} \beta=2$.Since the maximum value of $\sin ^{2} 	heta$ is $1$,the equation $\sin ^{2} \alpha+\sin ^{2} \beta=2$ can only hold if $\sin ^{2} \alpha=1$ and $\sin ^{2} \beta=1$.This implies $\sin \alpha = \pm 1$ and $\sin \beta = \pm 1$.For $\sin ^{2} \alpha=1$,$\alpha = \frac{\pi}{2}, \frac{3\pi}{2}, \dots$ and for $\sin ^{2} \beta=1$,$\beta = \frac{\pi}{2}, \frac{3\pi}{2}, \dots$.Taking the principal values,$\alpha = \frac{\pi}{2}$ and $\beta = \frac{\pi}{2}$.Substituting these values into the expression:$\cos \left(\frac{\alpha+\beta}{2}ight) = \cos \left(\frac{\frac{\pi}{2}+\frac{\pi}{2}}{2}ight) = \cos \left(\frac{\pi}{2}ight) = 0$.

If $\sin ^{2} \alpha+\sin ^{2} \beta=2,$ then the value of $\cos \left(\frac{\alpha+\beta}{2}\right)$ is

Similar Questions

If $\tan (A-B) = \frac{7}{24}$ and $\tan A = \frac{4}{3}$,where $A$ and $B$ are acute,then $A+B = $

If $7 \sin a = 24 \cos a$,then the value of $14 \tan a - 75 \cos a - 7 \sec a$ is equal to:

$\sin 50^\circ - \sin 70^\circ + \sin 10^\circ = $

What is the value of $\frac{\sin A - 2 \sin^3 A}{2 \cos^3 A - \cos A}$?

If $\sec \theta - \tan \theta = \frac{a+1}{a-1},$ then $\cos \theta =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module