# Answer to Question #4290 in Trigonometry 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

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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