If 4 ^2x=1 then the values of x are: - Vidyadip

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
$\text{n}\pi\pm\frac{\pi}{3},\text{n}\in\text{Z}$
✓
$\text{n}\pi\pm\frac{\pi}{6},\text{n}\in\text{Z}$
D
$2\text{n}\pi\pm\frac{\pi}{6},\text{n}\in\text{Z}$

✓

Answer

Correct option: C.

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

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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