What is the solution of sec x = tan x + cot x in the interval [0, 2pi]?

The question asks for the solution of sec x = tan x + cot
x in the interval [0,2pi].

=> sec x = tan x + cot
x

=> 1/cosx = (sin x/cos x )+ (cos x/ sin
x)

=> (sin x) (cos x) [1/cos x] = (sin x) (cos x) [
(sin x/cos x) +( cos x/sin x)]

=> sinx = sin^2(x) +
cos^2(x)

=> sinx =
1

The sin of 90 degrees is
1.

The solution is 90 degrees or
pi/2.