怎么证明tan^2x+cot^2x=2(3+cos4x)/1-cos4x

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怎么证明tan^2x+cot^2x=2(3+cos4x)/1-cos4x怎么证明tan^2x+cot^2x=2(3+cos4x)/1-cos4x怎么证明tan^2x+cot^2x=2(3+cos4x)

怎么证明tan^2x+cot^2x=2(3+cos4x)/1-cos4x
怎么证明tan^2x+cot^2x=2(3+cos4x)/1-cos4x

怎么证明tan^2x+cot^2x=2(3+cos4x)/1-cos4x
tan^2x+cot^2x=tan^2x+1/tan^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)