Question

Prove That

$\cot(x) \cot(2x) - \cot(2x) \cot(3x) - \cot(3x) \cot(x) = 1$

Class 11

Trigonometric Functions

Answer 1

HEYA!!
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Cot X •Cot 2X - Cot 2X• Cot 3X - Cot 3X •Cot X = 1

Taking Cot 3X common ,
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Cot X • Cot 2X - Cot 3X ( Cot 2X + Cot X )

Cot X • Cot 2X - Cot ( 2X + X ) ( Cot 2X + Cot X )



[ Using the identity Cot ( X + Y ) = Cot X Cot Y - 1 / Cot X + Cot Y ]

Cot X •Cot 2X - [ Cot 2X Cot X - 1 / Cot X + Cot 2X ] ( Cot 2X + Cot X )

= Cot X • Cot 2X - ( Cot 2X • Cot X - 1 )

= Cot X • Cot 2X - Cot 2X • Cot X + 1

= 1 = LHS.

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