Question

Prove that: cot x.cot 2x – cot2x.cot 3x – cot 3x.cot x = 1
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Answer 1

$\large\underline\blue{\bold{Given \:  Question}}$

$\rm \: Prove \: that : \: cotxcot2x - cot2xcot3x - cot3xcotx = 1$

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$\begin{gathered}\Large{\bold{\blue{\underline{Formula \: Used \::}}}} \end{gathered}$

$\boxed{ \pink{ \rm : \implies \:cot(x + y) = \dfrac{cotx \: coty - 1}{coty + cotx} }}$

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$\large\underline\blue{\bold{Solution :- }}$

Consider,

$\rm : \implies \:cot3x \: = cot(2x + x)$

$\rm : \implies \:cot3x = \dfrac{cot2x \: cotx - 1}{cot2x + cotx}$

$\rm : \implies \:cot3x \: cot2x \: + \: cot3x \: cotx \: = \: cot2x \: cotx \: - \: 1$

$\rm : \implies \:\: cotxcot2x - cot2xcot3x - cot3xcotx = 1$

$\large{\boxed{\boxed{\bf{Hence, Proved}}}}$

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