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22 February, 15:00

1 / (Sec x Tanx) = Sec x + tan x

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  1. 22 February, 15:26
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    Step-by-step explanation:

    to prove that 1 / (sec x - tan x) = sec x + tan x

    from the right hand side sec x + tan x =

    from trigonometry basics

    sec x = 1 / cos x

    tan x = sin x / cos x

    so, sec x + tan x = 1 / cosx + sinx / cosx

    finding the lcm

    = (1 + sinx) / cos x

    = (1 + sinx) cosx / cos²x

    = (1 + sinx) cosx / (1 - sinx) (1 + sinx)

    (1 + sinx) cancels the (1 - sinx) at the denominator

    so we have;

    = cos x / 1 - sinx

    1/1/cosx - sinx/cosx

    remember that 1 / cos x = sec x

    and also sinx/cos x = tan x

    so therefore we have 1 / sec x - tanx

    since LHS = RHS then we can say that 1 / sec x - tan x = sec x + tan x.
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