Упростить выражение: 1) cos(π/4 + a) × cos(π/4 - a) + 1/2sin²a 2) cos 2a - cos a × cos 3a

Question

Упростить выражение:

1) cos(π/4 + a) × cos(π/4 - a) + 1/2sin²a

2) cos 2a - cos a × cos 3a

Answer 1

1) Sin(a)*(1-Cos^2(a)) = Sin^2 (a) * Sin^2 (a) = Sin^4 (a)
2)Sin^4(a) + cos^4(a) + 2sin^2(a)(1-sin^2(a)) = Sin^4(a) + cos^4(a) + 2sin^2(a) - 2Sin^4(a) = cos^4(a) + 2sin^2(a) - Sin^4(a) = cos^4(a) + sin^2(a)*(2-Sin^2(a)) = cos^4(a) + sin^2(a)*(1+1-Sin^2(a)) = cos^4(a) + sin^2(a)*(1+Cos^2(a))
3)cos(a)*(Cos^2(a)+Sin^2(a)) = cos(a)
4)(cos^3(a)-sin^3(a))+(cos(a)sin^2(a)-sin(a)*cos^2(a))=(cos^3(a)-sin^3(a))+Cos(a)*Sin(a)*(Sin^2(a)-Cos^2(a)=Cos(a)*Sin(a)*(Cos^2(a)-Sin^2(a)+Sin^2(A)-Cos^2(a))=Cos(a)*Sin(a)*0=0