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Math Help - [SOLVED] Solving trig equations

  1. #1
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    [SOLVED] Solving trig equations

    Solve the equation (secx-cosx)^2=tanx-sin^2x on the interval -2\pi<x<2\pi

    I tried for ages but didn't manage to get very far, any help would be great.
    thanks
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by greghunter View Post
    Solve the equation (secx-cosx)^2=tanx-sin^2x on the interval -2\pi<x<2\pi

    I tried for ages but didn't manage to get very far, any help would be great.
    thanks
    When you foil out the left, you get

    \sec^2x-2+\cos^2x=\tan x-\sin^2x\implies \sec^2x-1-\left(1-\cos^2x\right)=\tan x-\sin^2x \implies \tan^2x-\sin^2x=\tan x-\sin^2x\implies \tan^2x=\tan x

    This now simplifies to \tan x\left(\tan x-1\right)=0\implies \tan x=0 or \tan x=1.

    Can you take it from here?
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  3. #3
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    thanks...annoyingly simple!
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