Question

proof of the identity sin(a+b)=sina.cosb +cosa.sinb ???

Answer 1

sin(A+B)=sinA cosB + cosA sinB

Answer 2

It must be given that a and b are complementary angles. L. H. S. =sin 90 degree=1.Since, a+b =90.Now,R.H.S. :sin(90-A)=cos A. Therefore, sin(90-b)=cos b=sin a. and cos(90-b)=cos a =sin b. Hence, sin^2b +cos ^2 b=1.Now,L.H.S.=R.H.S.Hence,proved.