Question
Download Solution PDFWhat is cot 2x cot 4x - cot 4x cot 6x - cot 6x cot 2x equal to
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
\(\rm cot (A + B) = \dfrac{cot A cot B - 1}{cot A + cot B}\)
Calculation:
Given,
(cot 2x ∙ cot 4x) - (cot 4x ∙ cot 6x) - (cot 6x ∙ cot 2x)
⇒ (cot 2x ∙ cot 4x) - cot 6x [cot 4x + cot 2x]
⇒ (cot 2x ∙ cot 4x) - cot (2x + 4x) [cot 4x + cot 2x]
⇒ (cot 2x ∙ cot 4x) - \((\rm \dfrac{cot 2x .cot 4x - 1}{cot 2x + cot 4x})\)× [cot 4x + cot 2x]
⇒ (cot 2x ∙ cot 4x) - (cot 2x ∙ cot 4 x - 1)
⇒ (cot 2x ∙ cot 4x) - (cot 2x ∙ cot 4x) + 1
⇒ 1
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