Упростите: sin²a+sin²b+cos(a+b)*cos(a-b)

Question

Упростите:
sin²a+sin²b+cos(a+b)*cos(a-b)

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