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NDA 2025 Maths · Mathematics · Trigonometric Equations · medium

The general solution of sin ^2x=1/4 is (where n is an integer)

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The general solution of sin⁡2x=14\sin^2x=\dfrac14 is (where nn is an integer)
  1. A. x=nπ±π6x=n\pi\pm\dfrac\pi6
  2. B. x=2nπ±π6x=2n\pi\pm\dfrac\pi6
  3. C. x=nπ+(−1)nπ6x=n\pi+(-1)^n\dfrac\pi6
  4. D. x=nπ±π3x=n\pi\pm\dfrac\pi3
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Answer: (A) x=nπ±π6x=n\pi\pm\dfrac\pi6

sin⁡2x=sin⁡2π6\sin^2x=\sin^2\frac\pi6 gives x=nπ±π6x=n\pi\pm\frac\pi6. The form 2nπ±π62n\pi\pm\frac\pi6 is the solution of cos⁡x=cos⁡π6\cos x=\cos\frac\pi6 and nπ+(−1)nπ6n\pi+(-1)^n\frac\pi6 solves only sin⁡x=12\sin x=\frac12; both miss solutions.
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