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If the value of tanθ + cotθ = √3, then find the value of tan6θ + cot6θ.1. -22. -13. -34. -4 |
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Answer» Correct Answer - Option 1 : -2 Given: tanθ + cotθ = √3 Formula used: a3 + b3 = (a + b)3 - 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. |
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