Question
Download Solution PDFα மற்றும் β ஆகியவை நேர்மறை கோணங்களாக இருந்தால் \(α + β = \dfrac{\pi}{4}\) எனில், (1 + tan α) (1 + tan β) எதற்குச் சமம்?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFகருத்து:
\(\rm \tan (α + β) = \dfrac {tan \alpha + tan \beta }{1 -tan \alpha \;tan \beta }\)
கணக்கீடுகள்:
கொடுக்கப்பட்டால், α மற்றும் β ஆகியவை நேர்மறை கோணங்களாகும், அதாவது \(α + β = \dfrac{\pi}{4}\) ,
⇒ \(\rm \tan (α + β) = \tan (\dfrac{\pi}{4})\)
⇒ \(\rm \dfrac {tan \alpha + tan \beta }{1 -tan \alpha \;tan \beta } = 1\)
⇒ \(\rm {tan \alpha + tan \beta }= 1 -tan \alpha \;tan \beta \)
⇒ \(\rm {tan \alpha +tan \alpha \;tan \beta + tan \beta } - 1 = 0 \)
⇒ \(\rm {tan \alpha +tan \alpha \;tan \beta + tan \beta } +1-2= 0 \)
⇒ \(\rm {tan \alpha +tan \alpha \;tan \beta + tan \beta } +1=2\)
⇒ \(\rm tan \alpha (1 +tan \beta ) + (1+tan \beta)=2\)
⇒ \(\rm (1+ tan \alpha )(1 +tan \beta )=2\)
எனவே, α மற்றும் β நேர்மறை கோணங்களாக இருந்தால், \(α + β = \dfrac{\pi}{4}\) , பின்னர் (1 + tan α) (1 + tan β) என்பது 2 க்கு சமம்.
Last updated on May 30, 2025
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