If sin A + sin B = x and cos A + cos B = y,th | vedclass

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

Question

(A) Given: $\sin A + \sin B = x$  $(1)$ and $\cos A + \cos B = y$  $(2)$. Using sum-to-product formulas: $2 \sin(\frac{A+B}{2}) \cos(\frac{A-B}{2}) =

Vedclass · Accepted Answer

$\frac{2xy}{x^2 + y^2}$

Vedclass · Answer

(A) Given: $\sin A + \sin B = x$  $(1)$ and $\cos A + \cos B = y$  $(2)$. Using sum-to-product formulas: $2 \sin(\frac{A+B}{2}) \cos(\frac{A-B}{2}) = x$  $(3)$ $2 \cos(\frac{A+B}{2}) \cos(\frac{A-B}{2}) = y$  $(4)$ Dividing $(3)$ by $(4)$: $	an(\frac{A+B}{2}) = \frac{x}{y}$. We know that $\sin(A+B) = \frac{2 	an(\frac{A+B}{2})}{1 + 	an^2(\frac{A+B}{2})}$. Substituting the value: $\sin(A+B) = \frac{2(x/y)}{1 + (x/y)^2} = \frac{2x/y}{(y^2 + x^2)/y^2} = \frac{2xy}{x^2 + y^2}$.

If $\sin A + \sin B = x$ and $\cos A + \cos B = y$,then $\sin(A + B) = $

Similar Questions

If $A$ lies in the third quadrant and $3 \tan A - 4 = 0$,then find the value of $5 \sin 2A + 3 \sin A + 4 \cos A$.

If $\cos x + \cos^2 x = 1$,then the value of $\sin^2 x + \sin^4 x$ is

If $2 \sinh^{-1}\left(\frac{a}{\sqrt{1-a^2}}\right)=\log \left(\frac{1+x}{1-x}\right)$,then $x$ is equal to

Let $\alpha = 3 + 4 + 8 + 9 + 13 + 14 + \dots$ up to $40$ terms. If $(\tan \beta)^{1020}$ is a root of the equation $x^2 + x - 2 = 0$, where $\beta \in (0, \frac{\pi}{2})$, then $\sin^2 \beta + 3 \cos^2 \beta$ is equal to:

If $\tan \theta + \sin \theta = m$ and $\tan \theta - \sin \theta = n,$ then

Vedclass Test Series

Exam Paper Generator

Online Exam Module