Question

If A and B are acute angles such that sin (A – B) = 0 and 2 cos (A + B) – 1 = 0, then find angles A and B.

Answer 1

sin (A – B) = 0   ...(Given)

`\implies` sin (A – B) = sin 0°  ...(∵ sin 0° = 0)

`\implies` A – B = 0  ...(i)

and 2 cos (A + B) – 1 = 0  ...(Given)

`\implies` 2 cos (A + B) = 1

`\implies` cos (A + B) = `1/2`

`\implies` cos (A + B) = cos 60°   ...`(∵ cos 60^circ = 1/2)`

`\implies` A + B = 60°    ...(ii)

On adding equations (i) and (ii), we get

2A = 60°

`\implies` A = 30°

Put this value in equation (i), we get

30° – B = 0

`\implies` B = 30°