y=2(sinA^6+cosA^6)-3(sinA^4+cosA^4),求y的值.向高手请教. 求详细解答过程.

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y=2(sinA^6+cosA^6)-3(sinA^4+cosA^4),求y的值.向高手请教.求详细解答过程.y=2(sinA^6+cosA^6)-3(sinA^4+cosA^4),求y的值.向高手请

y=2(sinA^6+cosA^6)-3(sinA^4+cosA^4),求y的值.向高手请教. 求详细解答过程.
y=2(sinA^6+cosA^6)-3(sinA^4+cosA^4),求y的值.
向高手请教.
求详细解答过程.

y=2(sinA^6+cosA^6)-3(sinA^4+cosA^4),求y的值.向高手请教. 求详细解答过程.
y = 2(sinA^6 + cosA^6) - 3(sinA^4 + cosA^4)
= (2sinA^6 - 3sinA^4) + (2cosA^6 - 3cosA^4)
= sinA^4*(2sinA^2 - 3) + cosA^4*(2cosA^2 - 3)
= sinA^4*[(1 - cos2A) - 3] + cosA^4*[(1 + cos2A) - 3]
= -sinA^4*(2 + cos2A) + cosA^4*(cos2A - 2)
= cos2A*(cosA^4 - sinA^4) - 2(sinA^4 + cosA^4)
= cos2A*(cosA^2 - sinA^2)(cosA^2 + sinA^2) - 2*[(sinA^2 + cosA^2)^2 - 2sinA^2*cosA^2]
= cos2A*cos2A - 2*[1 - 2*(sinA*cosA)^2]
= (cos2A)^2 - 2 + 4*(sinA*cosA)^2
= (cos2A)^2 - 2 + (sin2A)^2
= 1 - 2
= -1