sin^6+COS^6===sin^6+cos^6====

sin(x)^6+cos(x)^6 ＝[sin(x)^2+cos(x)^2]*[sin(x)^4-sin(x)^2*cos(x)^2+cos(x)^4] ＝sin(x)^4+2*sin(x)^2*cos(x)^2+cos(x)^4-3*sin(x)^2*cos(x)^2 ＝[sin(x)^2+cos(x)^2]^2-3*sin(x)^2*cos(x)^2 =1-3*sin(x)^2*cos(x)^2 =5/8+3/8*cos(4*x)

原式=(sin^2+cos^2)(sin^4-sin^2cos^2+cos^4)=sin^4-sin^2cos^2+cos^4=(sin^2+cos^2)^2-3sin^2cos^2 =1-3 X (1-cos2)/2 X (1+cos2)/2=1-3/4 X sin2^2=1-3/4 X (1-cos4)/2=5/8+3/8 cos4