If sin A+sin B=sqrt{3}(cos B-cos A),then sin | vedclass

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

Question

(A) Given,$\sin A+\sin B=\sqrt{3}(\cos B-\cos A)$.Rearranging the terms,we get $\sin A+\sqrt{3}\cos A=\sqrt{3}\cos B-\sin B$.Dividing both sides by $2

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(A) Given,$\sin A+\sin B=\sqrt{3}(\cos B-\cos A)$.Rearranging the terms,we get $\sin A+\sqrt{3}\cos A=\sqrt{3}\cos B-\sin B$.Dividing both sides by $2$,we have $\frac{1}{2}\sin A+\frac{\sqrt{3}}{2}\cos A=\frac{\sqrt{3}}{2}\cos B-\frac{1}{2}\sin B$.This can be written as $\sin A \cos \frac{\pi}{3}+\cos A \sin \frac{\pi}{3}=\sin \frac{\pi}{3} \cos B-\cos \frac{\pi}{3} \sin B$.Using the formula $\sin(x+y)=\sin x \cos y+\cos x \sin y$ and $\sin(x-y)=\sin x \cos y-\cos x \sin y$,we get $\sin(A+\frac{\pi}{3})=\sin(\frac{\pi}{3}-B)$.Thus,$A+\frac{\pi}{3}=\frac{\pi}{3}-B$,which implies $A=-B$.Now,$\sin 3A+\sin 3B = \sin 3(-B)+\sin 3B = -\sin 3B+\sin 3B = 0$.

If $\sin A+\sin B=\sqrt{3}(\cos B-\cos A)$,then $\sin 3A+\sin 3B$ is equal to

Similar Questions

If $\alpha, \beta, \gamma \in \left(0, \frac{\pi}{2}\right)$,then $\frac{\sin(\alpha + \beta + \gamma)}{\sin \alpha + \sin \beta + \sin \gamma}$ is

If $3 \cos \theta + 4 \sin \theta = 5$,then the value of $3 \sin \theta - 4 \cos \theta$ is:

If $\cos x+\cos y+\cos \alpha=0$ and $\sin x+\sin y+\sin \alpha=0$,then $\cot \left(\frac{x+y}{2}\right)$ is equal to

If $(\sin \theta - \operatorname{cosec} \theta)^2 + (\cos \theta + \sec \theta)^2 = 5$ and $\theta$ lies in the third quadrant,then $(\sin \theta + \cos \theta)^3 = $

If $\cos \left(\frac{\pi}{4}-x\right) \cos 2 x+\sin x \sin 2 x \sec x = \cos x \sin 2 x \sec x+\cos \left(\frac{\pi}{4}+x\right) \cos 2 x$,then a possible value of $\sec x$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module