Question

If cos A = 1/2, then what is the positive value of cos 1/2 A, in simplest radical form with a rational denominator?

Answer 1

Answer:

$\cos(\frac{1}{2}A) = {\frac{\sqrt{3}}{2}$

Step-by-step explanation:

Given

$\cos A = \frac{1}{2}$

Required

Determine $\cos(\frac{1}{2}A)$

To do this, we make use of the following identity

$\cos(\frac{1}{2}A) = \sqrt{\frac{\cos A+1}{2}}$

Substitute: $\cos A = \frac{1}{2}$

$\cos(\frac{1}{2}A) = \sqrt{\frac{\frac{1}{2}+1}{2}}$

Solve the numerator

$\cos(\frac{1}{2}A) = \sqrt{\frac{\frac{2+1}{2}}{2}}$

$\cos(\frac{1}{2}A) = \sqrt{\frac{\frac{3}{2}}{2}}$

Rewrite as:

$\cos(\frac{1}{2}A) = \sqrt{\frac{3}{2} * \frac{1}{2}}$

$\cos(\frac{1}{2}A) = \sqrt{\frac{3}{4}}$

Take square roots

$\cos(\frac{1}{2}A) = {\frac{\sqrt{3}}{2}$