Question

Find A and B if sin A + 2B = root 3/2 and cos A+B =1/2

Answer 1

Sin(A+2B)=root3 /2
Wkt,
$sin \frac{\pi}{3} = \frac{ \sqrt{3} }{2} \: \: \: \: \: \: \: - - - 1$
Also given that cos (A+B) = 1/2
Wkt, cos(pi/3) = 1/2. ........ 2
From 1 & 2, we get,
A+2B=pi/3
A+B=pi/3
On solving, A=pi/3, and B=0