Question
Download Solution PDFLet θ and ϕ be an acute angle such that sin θ = \(\frac{1}{\sqrt2}\) and cos ϕ = \(\frac{1}{3}\), the value of θ + ϕ is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFSolution:
Given, sin θ = \(\frac{1}{\sqrt{2}}\)
⇒ \(\theta=\frac{\pi}{4} \)
and cos ϕ = \(\frac{1}{3}\)
⇒ \(\frac{\pi}{3}<\phi <\frac{\pi}{2}\)
So that \(\frac{\pi}{3}+\theta <\phi+\theta <\frac{\pi}{2}+\theta \)
⇒ \(\frac{7\pi}{12} <\phi+\theta <\frac{3\pi}{4} \)
Last updated on Jun 17, 2025
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