Question

cot x cot 2x - cot 2x cot 3x - cot 3x cotx=1​

Answer 1

Answer:

cot x .cot 2 x - cot 2 x. cot 3 x - cot 3 x. cot x = 1 [ Proved ]

Step-by-step explanation:

Given :

cot x .cot 2 x - cot 2 x. cot 3 x - cot 3 x. cot x = 1

L.H.S. = cot x .cot 2 x - cot 2 x. cot 3 x - cot 3 x. cot x

= > We have  3 x as x + 2 x

cot 3 x = cot ( x + 2 x )

Using formula cot ( A + B ) = ( cot A. cot B - 1 ) / cot A + cot B

= > cos 3 x = cot x . cot 2 x - 1 / cot x + cot 2 x

= > cot 3 x (  cot x + cot 2 x ) = cot x. cot 2 x - 1

= >  cot 3 x. cot x + cot 3 x . cot 2 x =  cot x. cot 2 x - 1

= > cot x. cot 2 x - cot 2 x . cot 3 x - cot 3 x. cot x  = 1

= > R.H.S.

Since L.H.S. = R.H.S.

Hence proved.