Question

cos(a+b) =0.5 find the value of sin(a+b)
​

Answer 1

cos(a−b)=cosacosb+sinasinb

while sin(a+b)=sinacosb+cosasinb.

In this case, both are equal to 0.5, so

cosa cosb+sina sinb=sina cosb+cosa sinb .

Regrouping,

sina sinb−sina cosb=cosa sinb−cosa cosb

sina(sinb−cosb)=cosa(sinb−cosb).

Unless sinb−cosb=0,

we can divide both sides by that factor,

giving sina=cosa.

Hope it helps....