Find cos 2A if tan A = 5/12 and <A lies in quadrant III.

Answer 1

If A is in quadrant 3, then 2 A is in quadrant 1 or 2

5^2 + 12^2 = 169 = 13^3

so sin A = -5/13
and cos A = -12/13

cos 2A = cos^2 A - sin^2 A
= (144 - 25)/169 = 119/169