Question

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

Answer 1

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