MCQ
If $\sin A=\frac{1}{2}$, then the value of $\cot A$ is
- ✓$\sqrt{3}$
- B$\frac{1}{\sqrt{3}}$
- C$\frac{\sqrt{3}}{2}$
- D1
✓
Answer
Correct option: A.
$\sqrt{3}$
(a) : Given, $\sin A=\frac{1}{2}$
$
\because \quad \cos A=\sqrt{1-\sin ^2 A} \quad\left[\because \sin ^2 A+\cos ^2 A=1\right]
$
$
\Rightarrow \cos A=\sqrt{1-\left(\frac{1}{2}\right)^2}=\sqrt{1-\frac{1}{4}}=\sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{2}
$
Now, $\cot A=\frac{\cos A}{\sin A}=\frac{\sqrt{3} / 2}{1 / 2}=\sqrt{3}$
$
\because \quad \cos A=\sqrt{1-\sin ^2 A} \quad\left[\because \sin ^2 A+\cos ^2 A=1\right]
$
$
\Rightarrow \cos A=\sqrt{1-\left(\frac{1}{2}\right)^2}=\sqrt{1-\frac{1}{4}}=\sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{2}
$
Now, $\cot A=\frac{\cos A}{\sin A}=\frac{\sqrt{3} / 2}{1 / 2}=\sqrt{3}$
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