Question

Find 4cos2a, if
$\cos(a) = \frac{ \sqrt{3} }{2}$
​

Answer 1

If you mean to find 4 cos(2a), then recall the double angle identity for cosine:

cos(2x) = 2 cos²(x) - 1

so that

4 cos(2a) = 4 (2 cos²(x) - 1) = 4 (√3 - 1)