化简:2sin^4x+3\4sin^2(2x)+5cos^4x-1\2(cos4x+cos2x)
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/10/04 13:21:29
化简:2sin^4x+3\4sin^2(2x)+5cos^4x-1\2(cos4x+cos2x)
2sin^4x+3\4sin^2(2x)+5cos^4x-1\2 (cos4x+cos2x)
=2sin^4x+3\4sin^2(2x)+5cos^4x-1\2【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
=2sin^4x+3\4sin^2(2x)+5cos^4x-1\2【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
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