作业帮(1+sin4θ-cos4θ)/(1+sin4θ+cos4θ)-(1+sin4θ+cos4θ)/(1+sin4θ-cos
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/14 18:29:25
(1+sin4θ-cos4θ)/(1+sin4θ+cos4θ)-(1+sin4θ+cos4θ)/(1+sin4θ-cos4θ)
(1+sin4θ-cos4θ)/(1+sin4θ+cos4θ)-(1+sin4θ+cos4θ)/(1+sin4θ-cos4θ)
=(1+2sin2θcos2θ-1+2sin²2θ)/(1+2sin2θcos2θ+2cos²2θ-1)-(1+2sin2θcos2θ+2cos²2θ-1)/(1+2sin2θcos2θ-1+2sin²2θ)
=(sin2θcos2θ+sin²2θ)/(sin2θcos2θ+cos²2θ)-(sin2θcos2θ+cos²2θ)/(sin2θcos2θ+sin²2θ)
=sin2θ/cos2θ-cos2θ/sin2θ
=(sin²2θ-cos²2θ)/(sin2θcos2θ)
=-cos4θ/(1/2sin4θ)
=-2cos4θ/sin4θ
=-2cot4θ
=(1+2sin2θcos2θ-1+2sin²2θ)/(1+2sin2θcos2θ+2cos²2θ-1)-(1+2sin2θcos2θ+2cos²2θ-1)/(1+2sin2θcos2θ-1+2sin²2θ)
=(sin2θcos2θ+sin²2θ)/(sin2θcos2θ+cos²2θ)-(sin2θcos2θ+cos²2θ)/(sin2θcos2θ+sin²2θ)
=sin2θ/cos2θ-cos2θ/sin2θ
=(sin²2θ-cos²2θ)/(sin2θcos2θ)
=-cos4θ/(1/2sin4θ)
=-2cos4θ/sin4θ
=-2cot4θ
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