Answer
The answer w'll be obtained using formulas
sin(a+b) = (sina cosb) + (sinb cosa)
sin(a-b) = (sina cosb) - (sinb cosa)
Using the trigonometric formula of addition and subtraction of sine we will get the desired answer.
L.H.S = R.H.S
sinasinb = (sin(a+b) + sin(a-b)) / 2
as we know that sin(a-b) = sinacosb - sinbcosa
sinasinb = ( sin(a+b) + sinacosb - sinbcosa ) / 2
as we know that sin(a+b) = sinacosb + sinbcosa
sinasinb = (sinacosb + sinbcosa + sinacosb - sinbcosa ) / 2
sinasinb = 2sinacosb / 2
sinasinb = sinasinb
hence L.H.S = R.H.S
