find the following .. cot2x

Question

Let cos x = 7/8 with A in QIII and find the following.

cot 2x

Answer 1

cos x = 7/8

sin x = sqrt(1 - cos^2x) = sqrt(1 - 49/64) = sqrt(15/64) = sqrt(15)/8

tan x = sinx/cosx = sqrt(15)/7

tan2x = (2 * tanx) / (1 - tan^2x) = (2 *sqrt(15)/7)/(1 - 15/49) = (2*sqrt(15)/7)/(34/49)= (2*sqrt(15)/7)(49/34) =

(7 * sqrt(15))/17

cot2x = 1/tan2x = 17/(7 * sqrt(15)) = 17*sqrt(15)/105