Sin(a+b)sin(a-b)+cos^2a+sin^2b

Question

Sin(a+b)sin(a-b)+cos^2a+sin^2b

Answer 1

 =sina*cosb+cosasinb)(sinacosb-cosbsina)+(cos²a+sin²b)=
   sin²acos²b-cos²asin²b+cos²a+sin²b=sin²acos²b-(cos²asin²b-cos²a)+sin²b=
= sin²acos²b-cos²a(sin²b-1)+sin²b= sin²acos²b-cos²a(-cos²b)+sin²b=
= cos²b(sin²a+cos²a)+sin²b=cos²b+sin²b=1