1)
слева
справа
2)
слева
cos⁶α+sin⁶α=(cos²α+sin²α)³-3cos⁴αsin²α-3sin⁴αcos²α=1-3sin²αcos²α;
справа
3)
sin(π+α)=-sinα
sin((4π/3)+α)=sin(π+(π/3)+α)=-sin((π/3)+α)
sin((2π/3)+α)=sin(π-(π/3)+α)=sin((π/3)-α)
sin((π/3)+α)sin((π/3)-α)=(sin(π/3)cosα+cos(π/3)sinα)·(sin(π/3)cosα-cos(π/3)sinα)=
=(3/4)cos²α-(1/4)sin²α=(3/4)·(1-sin²α)-(1/4)sin²α=(3/4)-sin²α
слева
sin(π+α)sin((4π/3)+α)sin((2π/3)+α)=-sinα(-(3/4)+sin²α)=(3/4)sinα-sin³α
и справа
(1/4)sin3α= (3/4)sinα - sin³α