What is the solution of sec x = tan x + cot x in the interval [0, 2pi]?
1 Answer
academicsfirst | High School Teacher | (Level 2) Adjunct Educator
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.