高等数学化简这一步我化简了好多好多次,始终化简不出答案,

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高等数学化简这一步我化简了好多好多次,始终化简不出答案,
高等数学化简
这一步我化简了好多好多次,始终化简不出答案,

高等数学化简这一步我化简了好多好多次,始终化简不出答案,
如图

原式
=2sin(x+y)*cos (x+y)*[1-1/ sin²(x+y)]/ sin^4(x+y)
=2sin(x+y)*cos (x+y)*[ sin²(x+y)-1]/ [sin²(x+y)*sin^4(x+y)]
=2sin(x+y)*cos (x+y)*[-cos²(x+y)]/ [sin²(x+y)*sin^...

全部展开

原式
=2sin(x+y)*cos (x+y)*[1-1/ sin²(x+y)]/ sin^4(x+y)
=2sin(x+y)*cos (x+y)*[ sin²(x+y)-1]/ [sin²(x+y)*sin^4(x+y)]
=2sin(x+y)*cos (x+y)*[-cos²(x+y)]/ [sin²(x+y)*sin^4(x+y)]
= -2cos³(x+y)/sin^5(x+y)
= -2[1/sin²(x+y)]*[cos³(x+y)/sin³(x+y)]
= -2csc²(x+y)cot³(x+y)

收起

原式={2cos(x+y)*[-cot^2(x+y)]}/sin^3(x+y)
=[-2cot(x+y)*cot^2(x+y)]/sin^2(x+y)
=-2csc^2(x+y)cot^3(x+y)

如图