If $\cos A = \frac{1}{2}$, then the value of $\sin^2 A + 2\cos^2 A$...

Question

If $\cos A = \frac{1}{2}$, then the value of $\sin^2 A + 2\cos^2 A$ is:

Accepted Answer

$\sin^2 A + 2\cos^2 A = (\sin^2 A + \cos^2 A) + \cos^2 A = 1 + \cos^2 A = 1 + \left(\frac{1}{2}\right)^2 = 1 + \frac{1}{4} = \frac{5}{4}$.