Question

упростить выражение
sin(a-b)sin(a+b)+sin^2b+cos^2a

Answer 1

sin(a-b)sin(a+b)+sin²b+cos²a=

1/2(cos(a-b-a-b)-cos(a-b+a+b)+sin²b+

cos²a=1/2(cos(-2b)-cos2a)+(1-cos2b)/2+

+(1+cos2a)/2=1/2*cos2b-1/2*cos2a+1/2-

-1/2*cos2b+1/2+1/2*cos2a=1/2+1/2=1