If $\sin{x + \sin{y = a}}$ and $\cos{x + \cos{y = b}}$, then $ an\left( \frac{a + y}{2} ight)$ is equal to

Question

If $\sin{x + \sin{y = a}}$ and $\cos{x + \cos{y = b}}$, then $	an\left( \frac{a + y}{2} ight)$ is equal to

Dr. Abubacker · Accepted Answer

(b)
$\frac{\sin{x + \sin y}}{\cos{x + \cos y}} = \frac{a}{b}$
$\Rightarrow \ \ \ \frac{2\sin{\left( \frac{x + y}{2} ight)\cos\left( \frac{x - y}{2} ight)}}{2\cos{\left( \frac{x + y}{2} ight)\cos\left( \frac{x - y}{2} ight)}} = \frac{a}{b}$
$\Rightarrow \ 	an\left( \frac{x + y}{2} ight) = \frac{a}{b}$

Q. If $\sin{x + \sin{y = a}}$ and $\cos{x + \cos{y = b}}$, then $\tan\left( \frac{a + y}{2} \right)$ is equal to

Explanation

Reviewed by Dr. Abubacker

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