Question

Sin(a+b).cos(a-b) = sinacosa + sinbcosb

Answer 1

Sin (A + B) = sin A cos B + cos A Sin B 
Cos (A - B) = cos A cos B + sin A sin B 

=> (SinACosB+ CosASinB) (CosACosB +SinASinB) 

=>SinACosACos^2B+Sin^2ACosBSinB+Cos^2A... 

=>SinACosA(Cos^2B+Sin^2B) +SinBCosB(Sin^2A+Cos^2A) 
we know that Sin^2+Cos^2=1 
=>SinACosA(1)+SinBCosB(1) 
=SinACosA+SinBCosB 
Proved