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Prove that cot x cot 2 x-cot 2 x cot 3 x...

Prove that `cot x cot 2 x-cot 2 x cot 3 x-cot 3 x cot x=1`

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We know that .3 x=-2 x+x. .cot 3 x=cot (2 x+x).
.cot 3 x=(cot 2 x cot x-1)/(cot 2 x+cot x).
.[because . cot (x+y)=(cot x cot y-1)/(cot x+cot y)].
.cot 3 x(cot 2 x+cot x)=cot 2 x cot x-1. .cot 2 x cot 3 x+cot x cot 3 x=cot x cot 2 x-i. .cot x^(prime) cot 2 x-cot 2 x cot 3 x-cot 3 x cot x=1.
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