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Question
Prove the following:
cot x cot 2x – cot 2x cot 3x – cot 3x cot x = 1
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Solution
cot 3x = cot(2x + x) = `(cot 2x cot x-1)/(cot x + cot 2x)` `[∵ cot (A + B) = (cot A cot B - 1)/(cot A + cot B)]`
⇒ cot 3x (cot x + cot 2x) = cot 2x cot x - 1
⇒ cot 3x cot x + cot 3x cot 2x = cot 2x cot x - 1
⇒ cot x cot 2x - cot 2x cot 3x - cot 3x cot x = 1
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