How do you prove #(1-\cos^2 x)(1+\cot^2 x) = 1#?

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Answer 1 · 2014-10-24T09:43:54

By the trig identities

#cos^2x+sin^2x=1 Rightarrow sin^2x=1-cos^2x#

and

#1+cot^2x=csc^2x=1/{sin^2x}#,

we have

#(1-cos^2x)(1+cot^2x)=sin^2x cdot 1/{sin^2x}=1#.

I hope that this was helpful.