Suppose cos 2 A = 2/3 , and 2A is an angle in the Fourth Quadrant. Then cos A (exact value) =

Answer 1

Since 2A is in quadrant 4, 3π/2 < 2A < 2π. So, 3π/4 < A < π. Therefore, A lies in quadrant 2. So, cosA < 0.

Using the double angle formula cos2A = 2cos²A - 1, cos²A = (cos2A + 1) / 2 = 5/6.

So, cosA = ± √(5/6.

But, cosA < 0. So, cosA = -√(5/6) = - √30 / 6

Answer 2