Тригонометрия Помогите доказать, пожалуйста. Cos^6(п-a)+cos^6(п/2-a)=1/8(5+3cos4a)

Ответ. (cos(п-a))^6+(cos(п/2-a))^6=(1/8)*(5+3*cos(4*a));
(cos(a))^6+(sin(a))^6)=(1/8)*(5+3*cos(4*a)); (cos(a))^2+(sin(a))^2)*((cos(a))^4+(sin(a))^4-(sin(a)*cos(a))^2)=(1/8)*(5+3*cos(4*a)); ((cos(a))^4+(sin(a))^4-2*(sin(a)*cos(a))^2+(sin(a)*cos(a))^2)=(1/8)*(5+3*cos(4*a)); ((cos(a))^2-(sin(a))^2)^2+(sin(a)*cos(a))^2)=(1/8)*(5+3*cos(4*a));

(cos(2*a))^2+0,25*(sin(2*a))^2=(1/8)*(5+3*cos(4*a));

0,25+0,75*(cos(2*a))^2=(1/8)*(5+3*cos(4*a)); 0,25+0,375*(1+cos(4*a))=(1/8)*(5+3*cos(4*a));5/8+(3/8)*cos(4*a))=(1/8)*(5+3*cos(4*a));(1/8)*(5+3*cos(4*a))=(1/8)*(5+3*cos(4*a));