Question
Download Solution PDFजर tanθ + cotθ = √3 चे मूल्य असल्यास, तर tan6θ + cot6θ चे मूल्य शोधा.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिलेल्याप्रमाणे:
tanθ + cotθ = √3
वापरलेले सूत्र:
a3 + b3 = (a + b)3 - 3ab(a + b)
a2 + b2 = (a + b)2 - 2(a × b)
tanθ × cotθ = 1
गणना:
tanθ + cotθ = √3
दोन्ही बाजूंचा घन केल्यास, आपल्याला मिळते
(tanθ + cotθ)3 = (√3)3
⇒ tan3θ + cot3θ + 3 × tanθ × cotθ × (tanθ + cotθ) = 3√3
⇒ tan3θ + cot3θ + 3√3 = 3√3
⇒ tan3θ + cot3θ = 0
दोन्ही बाजूंचा वर्ग घेतल्यास
(tan3θ + cot3θ)2 = 0
⇒ tan6θ + cot6θ + 2 × tan3θ × cot3θ = 0
⇒ tan6θ + cot6θ + 2 = 0
⇒ tan6θ + cot6θ = - 2
∴ tan6θ + cot6θ चे मूल्य - 2 आहे.
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