Question

If sin A = `1/3`, sin B = `1/4` then find the value of sin (A + B) where A and B are acute angles.

Answer 1

Since A and B are acute angles, all the ratios are positive.

sin A = `1/3`; sin B = `1/4`; cos A = `(2sqrt2)/3`; cos B = `sqrt15/4`

∴ sin (A + B) = sin A cos B + cos A sin B

`= 1/3 * sqrt15/4 + (2sqrt2)/3 * 1/4`

`= sqrt15/12 + (2sqrt2)/12`

`= (sqrt15 + 2sqrt2)/12`