Using the addition or subtraction formulas for sine or cosine ... sin (a) sin (b) = (sin (a+b) + sin (a-b)) / 2

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