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NDA 2020 Maths · Mathematics · Trigonometric Equations · easy

The general solution of tan θ=-√3 is

Single correct option

The general solution of tan⁡θ=−3\tan\theta=-\sqrt3 is
  1. A. θ=nπ+π3\theta=n\pi+\dfrac\pi3
  2. B. θ=nπ−π3\theta=n\pi-\dfrac\pi3
  3. C. θ=2nπ±π3\theta=2n\pi\pm\dfrac\pi3
  4. D. θ=nπ+(−1)nπ3\theta=n\pi+(-1)^n\dfrac{\pi}{3}
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Answer: (B) θ=nπ−π3\theta=n\pi-\dfrac\pi3

tan⁡θ=tan⁡α\tan\theta=\tan\alpha gives θ=nπ+α\theta=n\pi+\alpha; here tan⁡(−π/3)=−3\tan(-\pi/3)=-\sqrt3, so θ=nπ−π/3\theta=n\pi-\pi/3. The form 2nπ±α2n\pi\pm\alpha belongs to cosine and nπ+(−1)nαn\pi+(-1)^n\alpha to sine equations.
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