Tan x + Cot x = 8 Cos 2x

Question

Find, in terms of pi, all the values of x between 0 and pi which satisfy the equation Tan x + Cot x = 8 Cos 2x

Answer 1

tan x + 1/tan x = (1+ tan ^2(x))/tan x

 

sec^2(x)/tan x

 

1/sin x cos x = 8 cos 2x

 

8 sin x cos x cos 2x =1

 

sin4x =1/2

 

4x= pi/6, 5pi/6

 

x= pi/24.

x= 5 pi/24