Question

If sinA+sinB=a and cosA+ cosB= b then the value of cos(A+B) is

Answer 1

Let SinA + SinB = a ------------(1)

and CosA + CosB = b ------------(2)

Sq the two eqns, and subtract (2)^2 - (1)^2

You will get, Cos2A+Cos2B+2Cos(A+B) = b²-a².

So, 2Cos(A+B)Cos(A-B)+2Cos(A+B) = b²-a².

or Cos(A+B){2Cos(A-B)+2} = b²-a² ----------------(3)

Now Sq the two eqns and add, ie (2)^2+(1)^2

You will get 2+2Cos(A-B) = a²+b² -----------[Use this in (3)]

You'd get Cos(A+B){a²+b²) = (b²-a²).

or Cos(A+B) = (b²-a²)/{a²+b²)

which is the answer.

hope it helps friend