Question
Download Solution PDFa cot θ + b cosec θ = p மற்றும் b cot θ + a cosec θ = q என்றால் p2 - q2 என்பது ______ க்கு சமம்.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFகொடுக்கப்பட்டது:
a cot θ + b cosec θ = p
b cot θ + a cosec θ = q
பயன்படுத்தப்படும் சூத்திரம்:
Cosec2 θ - cot2 θ = 1
கணக்கீடு:
a cot θ + b cosec θ = p
இருபுறமும் வர்க்கப்படுத்துதல்
(a cot θ + b cosec θ)2 = (p)2
a2 cot2 θ + b2 cosec2 θ + 2 × ab cot θ × cosec θ = p2 ----- (1)
b cot θ + a cosec θ = q
இருபுறமும் வர்க்கப்படுத்துதல்
(b cot θ + a cosec θ)2 = (q)2
b2 cot2 θ + a2 cosec2 θ + 2 × ab cot θ × cosec θ = q2 ----- (2)
சமன்பாடு (1) மற்றும் (2)ஐ கழித்தல்
⇒ (p2 - q2) = a2 cot2 θ + b2 cosec2 θ + 2 × ab × cot θ × cosec θ - (b2 cot2 θ + a2 cosec2 θ + 2 × ab × cot θ × cosec θ)
⇒ a2 cot2 θ - a2 cosec2 θ + b2 cosec2 θ - b2 cot2 θ
⇒ a2 (cot2 θ - cosec2 θ) + b2 (cosec2 θ - cot2 θ)
⇒ b2 - a2
∴ சரியான விருப்பம் 3.
Last updated on Jun 13, 2025
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