Question

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

Answer 1

Step-by-step explanation:

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.