If sin x + sin y = alpha and cos x + cos y = | vedclass

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

Question

(C) Given $\sin x + \sin y = \alpha$ and $\cos x + \cos y = \beta$. Using sum-to-product formulas: $2 \sin \left(\frac{x+y}{2}\right) \cos \left(\frac

Vedclass · Accepted Answer

$\frac{\alpha^2 + \beta^2}{2 \alpha \beta}$

Vedclass · Answer

(C) Given $\sin x + \sin y = \alpha$ and $\cos x + \cos y = \beta$. Using sum-to-product formulas: $2 \sin \left(\frac{x+y}{2}ight) \cos \left(\frac{x-y}{2}ight) = \alpha$ $2 \cos \left(\frac{x+y}{2}ight) \cos \left(\frac{x-y}{2}ight) = \beta$ Dividing the two equations: $	an \left(\frac{x+y}{2}ight) = \frac{\alpha}{\beta}$ Using the identity $\sin(x+y) = \frac{2 	an \left(\frac{x+y}{2}ight)}{1 + 	an^2 \left(\frac{x+y}{2}ight)}$: $\sin(x+y) = \frac{2(\alpha/\beta)}{1 + (\alpha/\beta)^2} = \frac{2 \alpha \beta}{\beta^2 + \alpha^2}$ Therefore,$\operatorname{cosec}(x+y) = \frac{1}{\sin(x+y)} = \frac{\alpha^2 + \beta^2}{2 \alpha \beta}$.

If $\sin x + \sin y = \alpha$ and $\cos x + \cos y = \beta$,then $\operatorname{cosec}(x + y) = $

Similar Questions

The expression $\tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ}$ is equal to

In a right-angled triangle,the hypotenuse is $2 \sqrt{2}$ times the perpendicular drawn from the opposite vertex. Then the other acute angles of the triangle are

If $\sin ^{2} \theta+3 \cos \theta=2,$ then $\cos ^{3} \theta+\sec ^{3} \theta$ is equal to

If $A+B+C+D=2 \pi$,then $\cos A-\cos B+\cos C-\cos D=$

If $\cos x = \frac{2 \cos y - 1}{2 - \cos y}$ where $x, y \in (0, \pi)$,then $\tan(x/2) \cot(y/2) =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module