求证(tanx)^2+1/(tanx)^2=2(3+cos4x)/(1-cos4x)

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求证(tanx)^2+1/(tanx)^2=2(3+cos4x)/(1-cos4x)求证(tanx)^2+1/(tanx)^2=2(3+cos4x)/(1-cos4x)求证(tanx)^2+1/(ta

求证(tanx)^2+1/(tanx)^2=2(3+cos4x)/(1-cos4x)
求证(tanx)^2+1/(tanx)^2=2(3+cos4x)/(1-cos4x)

求证(tanx)^2+1/(tanx)^2=2(3+cos4x)/(1-cos4x)
等式右边=2(3+cos4x)/(1-cos4x)
=(2+2cos²2x)/sin²2x
=2(2cos²2x+sin²2x)/sin²2x
=4/tan²2x+2
=4/[2tanx/(1-tan²x)]²+2
=(1-tanx)²/tan²x+2
=1/tan²x+tan²x
=左边