Question
Download Solution PDFযদি tanθ + cotθ -এর মান = √3 হয়, তবে tan6θ + cot6θ -এর মান কত হবে তা সন্ধান করুন।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFপ্রদত্ত:
tanθ + cotθ = √3
অনুসৃত সূত্র:
a3 + b3 = (a + b)3 - 3ab(a + b)
a2 + b2 = (a + b)2 - 2(a × b)
tanθ × cotθ = 1
গণনা:
tanθ + cotθ = √3
উভয়দিকে ঘন নিলে, আমরা পাই যে,
(tanθ + cotθ)3 = (√3)3
⇒ tan3θ + cot3θ + 3 × tanθ × cotθ × (tanθ + cotθ) = 3√3
⇒ tan3θ + cot3θ + 3√3 = 3√3
⇒ tan3θ + cot3θ = 0
উভয়দিকে বর্গ নেওয়া হলে,
(tan3θ + cot3θ)2 = 0
⇒ tan6θ + cot6θ + 2 × tan3θ × cot3θ = 0
⇒ tan6θ + cot6θ + 2 = 0
⇒ tan6θ + cot6θ = - 2
∴ tan6θ + cot6θ -এর মান হল - 2
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