Question

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

Answer 1

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

$\Rightarrow \frac{\text{(cot 2x cot x)-1}}{\text{cot 2x + cot x}}$

$\therefore$ cot 3x (cot 2x+ cot x)= (cot 2x. cot x)-1

$\Rightarrow$ cot 3x . cot 2x+ cot 3x . cot x = (cot 2x . cot x) -1

$\Rightarrow$ cot 3x cot 2x + cot 3x cot x - cot 2x cot x + 1= 0

$\therefore$ cot x cot 2x - cot 2x cot 3x - cot 3x. cot x

= 1
Hence proved.