Evaluate the values of x for tan^2x=(1+tanx)/2

We have to determine x given that (tan x)^2 = (1 + tan x)
/ 2.

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

multiply both sides by
2

=> 2 (tan x)^2  = 1 + tan
x

=> 2 (tan x)^2  - 1 - tan x
=0

=> 2 (tan x)^2 - 2 tan x + tan x -1
=0

=> 2 tan x ( tan x -1 ) + 1( tan x -1)
=0

=> (2 tan x + 1)( tan x - 1)
=0

=> (2 tan x + 1) = 0 or ( tan x - 1)
=0

=> tan x = -1/2  or tan x  =
1

Therefore x can take the values arc tan -1/2 and arc tan
1

or x = -26.56 + n*180 degrees or 45 + n*180
degrees.

The required values are x = -26.56 +
n*180 degrees or 45 + n*180 degrees.