Question

if sin A+ sin B = a and Cos A+ cosB= b then​

Answer 1

Answer:

Here is your answer

Step-by-step explanation:

(SinA+SinB)(CosA+CosB)

=SinACosA+SinACosB+SinBCosB)

=Sin2A+Sin2B)/2+Sin(A+B)=ab

Sin(A+B)=ab-(Sin2A+Sin2B)/2

Sin(A+B)=ab-Sin(A+B)Cos(A-B)

Sin(A+B)=ab/1+Cos(A-B)...(1)

(a^2=Sin^2A+Sin2^B+2SinASinB

b^2=Cos^2A+Cos^2B+2CosACosB

a^2+b^2=1+1+2/(SinASinB+CosA+CosB)

=2(1+SinASinB+CosACosB)

=2(1+Cos(A-B))=a^2+b^2

Cos(A-B)=a^2+b^2)/2-1