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Answer on Trigonometry Question for lissa

Question #4290
(1+1/tan^2x)(1+1/cot^2x)=1/sin^2x-sin^4x.please help me prove it.PLease
Expert's answer
(1+1/(tan x)^2)(1+1/(cotan x)^2)=1/(sin x)^2-(sin x)^4
1/(cos x)^2 * 1/(sin x)^2=1/(sin x)^2-(sin x)^4
1/(cos x)^2=1-(sin x)^6
(tan x)^2+(sin x)^6=0
tan x=0 and sin x=0
but it's not correct because we have tan x in the denominator. Hence given equality does not hold

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