Prove that cot x. cot 2x - cot 2x. cot3x - cot x. cot3x = 1.

The biggest angle is cot 3x = cot ( 2x+x )

Apply, cot (A+B) = (cot A.cot B -1)/ cot A + cot B

So, cot (3x) = ( cot 2x.cot x – 1 ) / cot 2x + cot x

Now, cross multiply

cot 3x ( cot 2x + cot x ) = cot 2x.cot x – 1 cot 2x.cot 3x + cot x.cot 3x

= cot 2x.cot x – 1 cot 2x.cot x – cot 2x.cot 3x – cot x.cot 3x

= 1

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