The general solution of cot θ + tan θ = 2 is

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Agniveer Vayu Group X 13 Oct 2023 Shift 1 Memory Based Paper
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  1. \(\theta = n\pi + {( - 1)^n}\frac{\pi }{8}\)
  2. \(\theta = \frac{{n\pi }}{2} + {( - 1)^n}\frac{\pi }{6}\)
  3. \(\frac{{n\pi }}{2} + {( - 1)^n}\frac{\pi }{4}\)
  4. \(\theta = \frac{{n\pi }}{2} + {( - 1)^n}\frac{\pi }{8}\)

Answer (Detailed Solution Below)

Option 3 : \(\frac{{n\pi }}{2} + {( - 1)^n}\frac{\pi }{4}\)
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Detailed Solution

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Calculation:

Given cot θ + tan θ = 2

\(\rm {1\over \tanθ} +\tan θ = 2\)

tan2 θ - 2 tan θ + 1 = 0

(tan θ - 1)2 = 0

tan θ = 1

θ = \({\pi\over4}, {5\pi\over4}, {9\pi\over4}...\) = \(\frac{{n\pi }}{2} + {( - 1)^n}\frac{\pi }{4}\), (n ∈ N)

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