Question

Question 2
If $sinA=\frac{1}{2}$, then the value of cot A is

(A) $\sqrt{3}$
(B) $\frac{1}{\sqrt{3}}$
(C) $\frac{\sqrt{3}}{2}$
(D) $1$

Answer 1

The answer is (A)
Thinking Process
i) First we use the formula $cos\theta =\sqrt{1-si{n}^2\theta }$ to get the value of $cos\theta$

ii) Now, we use the trigonometric ratio $cot\theta =\frac{cos\theta }{sin\theta }$ to get the value of $cot\theta$

Given, $sinA=\frac{1}{2}$,

$\therefore cosA=\sqrt{1-si{n}^{2}A}=\sqrt{1-{\left(\frac{1}{2}\right)}^2}$

$=\sqrt{1-\frac{1}{4}}=\sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{2}\lfloor \because si{n}^{2}A+co{s}^2=1\Rightarrow cosA=\sqrt{1-si{n}^{2}A}\rfloor$

Now, $cotA=\frac{cosA}{sinA}=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\sqrt{3}$

Hence, the required value of tan A is $\sqrt{3}$