given tanx= (1/2) and cscx<0, find cos2x

Answer 1

draw a triangle

legs are and 1 and 2, so hypotenuse = √5

csc = hyp/opp = √5/1 = √5

since csc < 0 and tan > 0, angle is in Q4.

sin = -1/√5

cos2x = 1 - 2sin^2(x) = 1 - 2*1/5 = 3/5