if tan x= negative 3/14 and pi/2< x<pi , find cos2x

Answer 1

The above sketch shows the situation. Using the Pythagorean Theorem, the hypotenuse is √205. Using the identity cos2x = cos^2x - sin^2x and the fact that cos(x) = -14/√205 and sin(x) = 3/√205, then cos(2x) = (-14/√205)² - (3/√205)² = 196/205 - 9/205 = 187/205