Simplify the expression for f(x)=(tan(x)-1)/(sec(x)) by writing it in terms of sin (x) and cos (x), and then find f'(x).

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The function f(x)=(tan x - 1)/(sec x)

f(x)=(tan x - 1)/(sec x)

=> (sin x/cos x - 1)/(1/cos x)

=> ((sin x - cos x)*cos x)/cos x

=> sin x - cos x

The derivative f'(x) = cos x + sin x