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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

We have cot 3x = cot (2x+x)

(cot 2x cot x)-1cot 2x + cot x

cot 3x (cot 2x+ cot x)= (cot 2x. cot x)-1

cot 3x . cot 2x+ cot 3x . cot x = (cot 2x . cot x) -1

cot 3x cot 2x + cot 3x cot x - cot 2x cot x + 1= 0

cot x cot 2x - cot 2x cot 3x - cot 3x. cot x

= 1
Hence proved.


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