If sin A + sin B = C and cos A + cos B = D,th | vedclass

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

Question

(D) Given: $\sin A + \sin B = C$ and $\cos A + \cos B = D$.Dividing the two equations:$\frac{\sin A + \sin B}{\cos A + \cos B} = \frac{C}{D}$Using the

Vedclass · Accepted Answer

$\frac{2CD}{C^2 + D^2}$

Vedclass · Answer

(D) Given: $\sin A + \sin B = C$ and $\cos A + \cos B = D$.Dividing the two equations:$\frac{\sin A + \sin B}{\cos A + \cos B} = \frac{C}{D}$Using the sum-to-product formulas:$\frac{2 \sin \frac{A + B}{2} \cos \frac{A - B}{2}}{2 \cos \frac{A + B}{2} \cos \frac{A - B}{2}} = \frac{C}{D}$$	an \frac{A + B}{2} = \frac{C}{D}$Now,using the double angle formula in terms of tangent:$\sin (A + B) = \frac{2 	an \frac{A + B}{2}}{1 + 	an^2 \frac{A + B}{2}}$Substituting $	an \frac{A + B}{2} = \frac{C}{D}$:$\sin (A + B) = \frac{2(C/D)}{1 + (C/D)^2} = \frac{2C/D}{(D^2 + C^2)/D^2} = \frac{2CD}{C^2 + D^2}$.

If $\sin A + \sin B = C$ and $\cos A + \cos B = D$,then the value of $\sin (A + B) = $

Similar Questions

If $2 \sin \theta + \cos \theta = \frac{7}{3},$ then the value of $(\tan^2 \theta - \sec^2 \theta)$ is

$\sin^{2} \theta = \frac{(x+y)^{2}}{4xy}$ is possible only when

If $\theta$ is an acute angle and $\sin \frac{\theta}{2} = \sqrt{\frac{x - 1}{2x}}$,then $\tan \theta$ is equal to

The value of $\sin^2 \frac{\pi}{8} + \sin^2 \frac{3\pi}{8} + \sin^2 \frac{5\pi}{8} + \sin^2 \frac{7\pi}{8}$ is

If the maximum value of $y = \frac{7 + 6 \tan x - \tan^2 x}{1 + \tan^2 x}$ is $\lambda$,then the value of $\log_{\sqrt{2}}(\lambda)$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module