Question
Download Solution PDFtanθ + cotθ = √3, ആണെങ്കിൽ tan6θ + cot6θ ന്റെ മൂല്യം കണ്ടെത്തുക.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFനൽകിയിരിക്കുന്നത്:
tanθ + cotθ = √3
ഉപയോഗിച്ച സൂത്രവാക്യം:
a3 + b3 = (a + b)3 - 3ab(a + b)
a2 + b2 = (a + b)2 - 2(a × b)
tanθ × cotθ = 1
കണക്കുകൂട്ടൽ:
tanθ + cotθ = √3
സമവാക്യത്തിന്റെ ഇരു വശങ്ങളിലും ത്രിവര്ഗ്ഗം കാണുമ്പോൾ
(tanθ + cotθ)3 = (√3)3
⇒ tan3θ + cot3θ + 3 × tanθ × cotθ × (tanθ + cotθ) = 3√3
⇒ tan3θ + cot3θ + 3√3 = 3√3
⇒ tan3θ + cot3θ = 0
സമവാക്യത്തിന്റെ ഇരു വശങ്ങളിലും വര്ഗ്ഗം കാണുമ്പോൾ
(tan3θ + cot3θ)2 = 0
⇒ tan6θ + cot6θ + 2 × tan3θ × cot3θ = 0
⇒ tan6θ + cot6θ + 2 = 0
⇒ tan6θ + cot6θ = - 2
∴ tan6θ + cot6θ ന്റെ മൂല്യം - 2 ആണ്.
Last updated on Jun 10, 2025
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