化简:2sin^4x+3\4sin^2(2x)+5cos^4x-1\2(cos4x+cos2x)

1个回答

  • 2sin^4x+34sin^2(2x)+5cos^4x-12 (cos4x+cos2x)

    =2sin^4x+34sin^2(2x)+5cos^4x-12【cos^4(x)+sin^4(x)-6sin^2(x)cos^2(x)+cos^2(x)-sin^2(x)】

    =【3/2sin^4(x)+6sin^2(x)cos^2(x)+9/2cos^4(x)】 - 1/2 cos^2(x) +1/2 sin^2(x)

    =【[(3/2sin^2(x)+9/2cos^2(x)][sin^2(x)+cos^2(x)]】 - 1/2 cos^2(x)+1/2 sin^2(x)

    =【[3/2+3cos^2(x)] * 1】- 1/2 cos^2(x)+1/2 sin^2(x)

    =3/2+【5/2 cos^2(x)+1/2 sin^2(x)】

    =3/2+【1+3/2cos^2(x)】

    =5/2+3/2cos^2(x)

    黑体中括号为主要变换部分