Given that cos left( frac{alpha - beta}{2} ri | vedclass

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

Question

(B) Given: $\cos \left( \frac{\alpha - \beta}{2} \right) = 2\cos \left( \frac{\alpha + \beta}{2} \right)$ Using the expansion formulas $\cos(A-B) = \c

Vedclass · Accepted Answer

$\frac{1}{3}$

Vedclass · Answer

(B) Given: $\cos \left( \frac{\alpha - \beta}{2} ight) = 2\cos \left( \frac{\alpha + \beta}{2} ight)$ Using the expansion formulas $\cos(A-B) = \cos A \cos B + \sin A \sin B$ and $\cos(A+B) = \cos A \cos B - \sin A \sin B$: $\cos \frac{\alpha}{2} \cos \frac{\beta}{2} + \sin \frac{\alpha}{2} \sin \frac{\beta}{2} = 2 \left( \cos \frac{\alpha}{2} \cos \frac{\beta}{2} - \sin \frac{\alpha}{2} \sin \frac{\beta}{2} ight)$ $\cos \frac{\alpha}{2} \cos \frac{\beta}{2} + \sin \frac{\alpha}{2} \sin \frac{\beta}{2} = 2 \cos \frac{\alpha}{2} \cos \frac{\beta}{2} - 2 \sin \frac{\alpha}{2} \sin \frac{\beta}{2}$ Rearranging the terms: $3 \sin \frac{\alpha}{2} \sin \frac{\beta}{2} = \cos \frac{\alpha}{2} \cos \frac{\beta}{2}$ Dividing both sides by $3 \cos \frac{\alpha}{2} \cos \frac{\beta}{2}$: $\frac{\sin \frac{\alpha}{2} \sin \frac{\beta}{2}}{\cos \frac{\alpha}{2} \cos \frac{\beta}{2}} = \frac{1}{3}$ $	an \frac{\alpha}{2} 	an \frac{\beta}{2} = \frac{1}{3}$

Given that $\cos \left( \frac{\alpha - \beta}{2} \right) = 2\cos \left( \frac{\alpha + \beta}{2} \right)$,then $\tan \frac{\alpha}{2} \tan \frac{\beta}{2}$ is equal to

Similar Questions

In triangle $ABC$,if $\cos A \cos B + \sin A \sin B \sin C = 1$,then $\sin A + \sin B + \sin C =$

If $A+B+C=270^{\circ}$,then $\cos 2A + \cos 2B + \cos 2C + 4 \sin A \sin B \sin C =$

If the range of $f(\theta) = \frac{\sin^4 \theta + 3 \cos^2 \theta}{\sin^4 \theta + \cos^2 \theta}$,$\theta \in R$ is $[\alpha, \beta]$,then the sum of the infinite $G.P.$,whose first term is $64$ and the common ratio is $\frac{\alpha}{\beta}$,is equal to...........

The maximum value of $3 \cos \theta + 5 \sin \left( \theta - \frac{\pi}{6} \right)$ for any real value of $\theta$ is

The value of $k$,for which $(\cos x + \sin x)^2 + k \sin x \cos x - 1 = 0$ is an identity,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module