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

RHS = 1


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


LHS = RHS


Hence, proved.


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