मान लीजिए θ और ϕ न्यून कोण हैं जैसे कि sin θ  = \(\frac{1}{\sqrt2}\) और cos ϕ = \(\frac{1}{3}\), तो θ + ϕ का मान है:

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AAI ATC Junior Executive 27 July 2022 Shift 1 Official Paper
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  1. \(\left( {\frac{{5\pi }}{{12}},\frac{{3\pi }}{4}} \right)\)
  2. \(\left( {\frac{{7\pi }}{{12}},\frac{{3\pi }}{4}} \right)\)
  3. \(\left( {\frac{{\pi }}{{6}},\frac{{\pi }}{2}} \right)\)
  4. \(\left( {\frac{{\pi }}{{3}},\frac{{\pi }}{2}} \right)\)

Answer (Detailed Solution Below)

Option 2 : \(\left( {\frac{{7\pi }}{{12}},\frac{{3\pi }}{4}} \right)\)
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हल:

दिया गया है, sin θ = \(\frac{1}{\sqrt{2}}\)

⇒ \(\theta=\frac{\pi}{4} \)

और cos ϕ = \(\frac{1}{3}\)

⇒ \(\frac{\pi}{3}<\phi <\frac{\pi}{2}\)

इसलिए \(\frac{\pi}{3}+\theta <\phi+\theta <\frac{\pi}{2}+\theta \)

⇒ \(\frac{7\pi}{12} <\phi+\theta <\frac{3\pi}{4} \)

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