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

Question

Philoid · Accepted Answer

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.