MCQ
If $4\sin^2\text{x}=1$ then the values of x are:
  • A
    $2\text{n}\pi\pm\frac{\pi}{3},\text{n}\in\text{Z}$
  • B
    $\text{n}\pi\pm\frac{\pi}{3},\text{n}\in\text{Z}$
  • C
    $\text{n}\pi\pm\frac{\pi}{6},\text{n}\in\text{Z}$
  • D
    $2\text{n}\pi\pm\frac{\pi}{6},\text{n}\in\text{Z}$

Answer

  1. $\text{n}\pi\pm\frac{\pi}{6},\text{n}\in\text{Z}$

Solution:

Given:

$\Rightarrow\sin^2\text{x}=1$

$\Rightarrow\sin^2\text{x}=\frac{1}{4}$

$\Rightarrow\sin\text{x}=\frac{1}{2}$ or $\sin\text{x}=-\frac{1}{2}$

$\Rightarrow\sin\text{x}=\sin\frac{\pi}{6}$ or $\sin\text{x}=\sin\Big(-\frac{\pi}{6}\Big)$

$\Rightarrow\text{x}=\text{n}\pi+(-1)^\text{n}\frac{\pi}{6},\text{n}\in\text{Z}$ or $\text{n}\pi+(-1)^\text{n}\Big(-\frac{\pi}{6}\Big),\text{n}\in\text{Z}$

$\Rightarrow\text{x}=\text{n}\pi\pm\frac{\pi}{6},\text{n}\in\text{Z}$

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