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8. Introduction to Trigonometry
easy
If $\sin A =\frac{1}{2},$ then the value of $\cot A$ is
A
$\frac{1}{\sqrt{3}}$
B
$\sqrt{3}$
C
$\frac{\sqrt{3}}{2}$
D
$1$
Solution
Given, $\quad \sin A=\frac{1}{2}$
$\cos A=\sqrt{1-\sin ^{2} A}=\sqrt{1-\left(\frac{1}{2}\right)^{2}}$
$=\sqrt{1-\frac{1}{4}}=\sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{2}$ $[\because \sin ^{2} A+\cos ^{2}=1 \Rightarrow \cos A=\sqrt{1-\sin ^{2} A}]$
Now, $\quad \cot A=\frac{\cos A}{\sin A}=\frac{2}{1}=\sqrt{3}$
Standard 10
Mathematics
