Find the exact simplified value of cos(x/2) assuming that tan(x) = -5/12 and that 90° < x < 180°

Answer 1

45° < x/2 < 90°, x/2 is in quadrant I.

cos(x/2) = ((1 + cos(x))/2)^1/2;

cos(x) = - (1 + tan²(x))^-1/2 = - (1 + 25/144)^-1/2 = - 12/13;

cos(x/2) = ((1 - 12/13)/2)^1/2 = 1/(26)^1/2..