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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 have .3 x=2 x+x rarr cot 3 x=cot (2 x+x) rarr cot 3 x .=(cot 2 x cot x-1)/(cot x+cot 2 x).
.rarr cot 3 x cot x+cot 3 x cot 2 x=cot 2 x cot x-1 . rarr cot x cot 2 x-cot 2 x cot 3 x-cot 3 x cot x=1.
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