If $\frac{\cos A}{3} = \frac{\cos B}{4} = \frac{1}{5},\ - \frac{\pi}{2}

Question

If $\frac{\cos A}{3} = \frac{\cos B}{4} = \frac{1}{5},\ - \frac{\pi}{2} < A < 0,\ - \frac{\pi}{2} < B < 0$ then the value of $2\sin{A + 4\sin B}$ is

Dr. Abubacker · Accepted Answer

(c)
$\cos{A = \frac{3}{5},\cos{B = \frac{4}{5}}}$
$\because\ \ \angle A$ and $\angle B$ lie on 4^{th} quadrant
$	herefore\sin{A = - \sqrt{1 - \frac{9}{25}}},\sin{B = - \sqrt{1 - \frac{16}{25}}}$
⇒$\ \sin{A = - \frac{4}{5},\ \sin{B = - \frac{3}{5}}}$
$	herefore 2\sin{A + 4\sin B}$
$= 2\left( - \frac{4}{5} ight) + 4\left( - \frac{3}{5} ight)$
$= - \frac{8}{5} - \frac{12}{5}$
$= - \frac{20}{5} = - 4$

Q. If $\frac{\cos A}{3} = \frac{\cos B}{4} = \frac{1}{5},\ - \frac{\pi}{2} < A < 0,\ - \frac{\pi}{2} < B < 0$ then the value of $2\sin{A + 4\sin B}$ is

Explanation

Reviewed by Dr. Abubacker

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