# Prove that:  cot x cot 2x – cot 2x cot 3x – cot 3x cot x = 1

To prove:  cot x cot 2x – cot 2x cot 3x – cot 3x cot x = 1

Formula to use:

Proof :

LHS = cot x cot 2x – cot 2x cot 3x – cot 3x cot x

= cot x cot 2x – cot 3x (cot 2x + cot x)

= cot x cot 2x – cot (2x + x) (cot 2x + cot x)

LHS = cot x cot 2x – (cot x cot 2x – 1)

= cot x cot 2x – cot x cot 2x + 1

= 1

R.H.S = 1

∴ LHS = RHS

Hence, proved.

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