Question

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

Answer 1

The answer w'll be obtained using formulas

cos(a+b) = cosacosb - sinasinb

cos(a-b) = cosacosb + sinasinb

Explanation:

Using the trigonometric formula of addition and subtraction of cosine

cos(a+b) = cosacosb - sinasinb

cos(a-b) = cosacosb + sinasinb

w'll get the desired answer.

To be solve

L.H.S = R.H.S

sinasinb = (cos(a-b)-cos(a+b)/2

as we know that cos(a+b) = cosacosb - sinasinb

sinasinb = (cos(a-b) - (cosacosb -sinasinb))/2

as we know that cos(a-b) = cosacosb + sinasinb

sinasinb = ((cosacosb + sinasinb) - (cosacosb -sinasinb))/2

sinasinb = (cosacosb + sinasinb - cosacosb + sinasinb)/2

sinasinb = (2sinasinb)/2

sinasinb = sinasinb

hence L.H.S = R.H.S