Question
Download Solution PDFIf the value of tanθ + cotθ = √3, then find the value of tan6θ + cot6θ.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
tanθ + cotθ = √3
Formula used:
(a + b)3 = a3 + b3 + 3ab(a + b)
a2 + b2 = (a + b)2 - 2(a × b)
tanθ × cotθ = 1
Calculation:
tanθ + cotθ = √3
Taking cube on both sides, we get
(tanθ + cotθ)3 = (√3)3
⇒ tan3θ + cot3θ + 3 × tanθ × cotθ × (tanθ + cotθ) = 3√3
⇒ tan3θ + cot3θ + 3√3 = 3√3
⇒ tan3θ + cot3θ = 0
Taking square on the both sides
(tan3θ + cot3θ)2 = 0
⇒ tan6θ + cot6θ + 2 × tan3θ × cot3θ = 0
⇒ tan6θ + cot6θ + 2 = 0
⇒ tan6θ + cot6θ = - 2
∴ The value of tan6θ + cot6θ is - 2.
Last updated on Jun 13, 2025
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