Prove the following: cot x cot 2x - cot 2x cot 3x - cot 3x cot x = 1

Solution:

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)

= cot x cot 2x - [(cot 2x cot x - 1) / (cot 2x + cot x)] (cot 2x + cot x)     [As cot (A + B) = (cot A cot B - 1) / (cot A + cot B) ]

= cot x cot 2x - [cot 2x cot x - 1]

= cot x cot 2x - cot 2x cot x + 1

= 1

= RHS

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.3 Question 22

Prove the following: cot x cot 2x - cot 2x cot 3x - cot 3x cot x = 1

Summary:

We got, cot x cot 2x - cot 2x cot 3x - cot 3x cot x = 1. Hence Proved