if tanx=a/b,prove that asin2x+bcos2x=b............prove it

Since tanx=a/b =>a = btanx...(1)Now, asin2x + bcos2x = a(2sinxcosx) + b(1- sin^2x)=2asinxcosx + b - bsin^2x=2sinx (acosx - bsinx) + b=2sinx (btanxcosx - bsinx) + b ...(from (1))=2sinx (bsinx - bsinx) + b=2sinx (0) + b=bHence, proved.