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19 May, 16:47

Find all solutions in the interval [0, 2π). tan x + sec x = 1

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  1. 19 May, 18:25
    0
    Use the identity

    sec^2x = 1 + tan^2 x

    - so sec x = sqrt (1 + tan^2 x) then:-

    tan x + sqrt (1 + tan^2 x) = 1

    sqrt (1 + tan^2 x) = 1 - tan x

    1 + tan^2 x = 1 + tan^2x - 2 tan x

    0 = - 2 tanx

    tan x = 0

    x = 0, π

    π is an extraneous root because sec 180 = - 1

    So the answer is 0 degrees
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