Question
Download Solution PDFtanθ + cotθ = √3 எனில், tan6θ + cot6θ இன் மதிப்பைக் கண்டறியவும்
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFகொடுக்கப்பட்டது:
tanθ + cotθ = √3
பயன்படுத்தப்பட்ட சூத்திரம்:
a3 + b3 = (a + b)3 - 3ab(a + b)
a2 + b2 = (a + b)2 - 2(a × b)
tanθ × cotθ = 1
கணக்கீடு:
tanθ + cotθ = √3
இரு பக்கங்களிலும் மும்மடிப் பெருக்கம் எடுக்கையில்,
(tanθ + cotθ)3 = (√3)3
⇒ tan3θ + cot3θ + 3 × tanθ × cotθ × (tanθ + cotθ) = 3√3
⇒ tan3θ + cot3θ + 3√3 = 3√3
⇒ tan3θ + cot3θ = 0
இரு பக்கங்களிலும் வர்க்கம் எடுக்கையில்,
(tan3θ + cot3θ)2 = 0
⇒ tan6θ + cot6θ + 2 × tan3θ × cot3θ = 0
⇒ tan6θ + cot6θ + 2 = 0
⇒ tan6θ + cot6θ = - 2
∴ tan6θ + cot6θ இன் மதிப்பு - 2 ஆகும்.
Last updated on Jul 8, 2025
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