Question
Download Solution PDFयदि tanθ + cotθ का मान = √3 है, तो tan6θ + cot6θ का मान ज्ञात कीजिये।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
tanθ + cotθ = √3
प्रयुक्त सूत्र:
(a + b)3 = a3 + b3 + 3ab(a + b)
a2 + b2 = (a + b)2 - 2(a × b)
tanθ × cotθ = 1
गणना:
tanθ + cotθ = √3
दोनों ओर का घन लेने पर, हमें प्राप्त होता है
(tanθ + cotθ)3 = (√3)3
⇒ tan3θ + cot3θ + 3 × tanθ × cotθ × (tanθ + cotθ) = 3√3
⇒ tan3θ + cot3θ + 3√3 = 3√3
⇒ tan3θ + cot3θ = 0
दोनों ओर का वर्ग लेने पर
(tan3θ + cot3θ)2 = 0
⇒ tan6θ + cot6θ + 2 × tan3θ × cot3θ = 0
⇒ tan6θ + cot6θ + 2 = 0
⇒ tan6θ + cot6θ = - 2
∴ tan6θ + cot6θ का मान - 2 है।
Last updated on Jul 19, 2025
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