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prove that
_______1______ - ___1___ =__1___
sec x-tan x cos x cos x
- _______1______
sec x + tan x

  • maths -

    I will rewrite the question as:

    1/(sec(x)-tan(x)) - 1/cos(x) = 1/(cos(x) - 1/(sec(x)+tan(x))

    transpose terms to get:
    1/(sec(x)-tan(x)) + 1/(sec(x)+tan(x)) = 2/cos(x)

    Add the two fractions on the left and simplify using sec2(x)=1+tan2(x) on the left-hand side to get 2sec(x)=2/cos(x).

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