If sin A = $\frac{1}{2}$, then the value of cot A is ______.

Question

KollegeApply · Accepted Answer

If sin A = $\frac{1}{2}$, then the value of cot A is underlinebb(sqrt(3)). Explanation: According to the question, sin A = $\frac{1}{2}$ ...(1) We know that, cot A = 1/(tan A) = (cos A)/(sin A) ...(2) To find the value of cos A. We have the equation, sin2 $\theta$ + cos2 $\theta$ = 1 So, cos $\theta$ = sqrt(1 - sin^2$\theta$) Then, cos A = sqrt(1 - sin^2A) ...(3) cos2A = 1 – sin2A cos A = sqrt(1 - sin^2A) Substituting equation 1 in 3, we get, cos A = sqrt(1 - $\frac{1}{4}$) = sqrt($\frac{3}{4}$) = sqrt(3)/2 Substituting values of sin A and cos A in equation 2, we get cot A = (sqrt(3)/2) xx 2 = sqrt(3)

AChoose Your Answer