How do you prove $cot^2 A csc^2 A - cot^2 A = cot^4 A$ ?

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Answer 1 · 2015-05-15T14:48:37

Replace cot by $cos/sin$ in left side.

$(cos^2 x/sin^2 x)(1/sin^2 x) - (cos^2 x/sin^2 x)$ =

$= ((cos^2 x)(1 - sin^2 x))/(sin^4 x)$ = $cos^4 x/sin^4 x = cot^4 x$

How do you prove cot^2 A csc^2 A - cot^2 A = cot^4 Acot^2 A csc^2 A - cot^2 A = cot^4 A?