求证:tan^2x+cot^2x=2(3+cos4x)/(1-cos4x)

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求证:tan^2x+cot^2x=2(3+cos4x)/(1-cos4x)求证:tan^2x+cot^2x=2(3+cos4x)/(1-cos4x)求证:tan^2x+cot^2x=2(3+cos4x

求证:tan^2x+cot^2x=2(3+cos4x)/(1-cos4x)
求证:tan^2x+cot^2x=2(3+cos4x)/(1-cos4x)

求证:tan^2x+cot^2x=2(3+cos4x)/(1-cos4x)
tan^2x+cot^2x=[(sinx)^4+(cosx)^4]/(sinxcosx)^2
={[(sinx)^2+(cosx)^2]^2-2(sinxcosx)^2}/(sinxcosx)^2
=[1-2(sinxcosx)^2]/(sinxcosx)^2
=4[1-1/2(sin2x)^2]/(sin2x)^2
=2[4-2(sin2x)^2]/(1-cos4x)
=2(3+cos4x)/(1-cos4x)
得证