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

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academicsfirst | High School Teacher | (Level 2) Adjunct Educator

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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.

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