Q. 224.2( 128 Votes )

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

Answer :

To prove:  cot x cot 2x – cot 2x cot 3x – cot 3x cot x = 1

Formula to use: 

Proof : 

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

R.H.S = 1

∴ LHS = RHS


Hence, proved.

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