(1+sin4θ-cos4θ)/(1+sin4θ+cos4θ)-(1+sin4θ+cos4θ)/(1+sin4θ-cos4θ)

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/27 22:22:19
(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+sin4θ-cos4θ)/(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+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