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Math Help - help with trig equations

  1. #1
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    Post help with trig equations

    hi everyone, I'm new so I hope I am doing this right.

    I don't know how to solve this problem:

    Use the algebraic method to write √2 sin x - √2 cos x in the form kcos(x + ϕ) where k>0, 0≤ ϕ ≤ 2π

    thanks for any help!
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  2. #2
    MHF Contributor red_dog's Avatar
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    \sqrt{2}\sin x-\sqrt{2}\cos x=-2\left(\frac{\sqrt{2}}{2}\cos x-\frac{\sqrt{2}}{2}\sin x\right)=
    =-2\left(\cos x\cos\frac{\pi}{4}-\sin x\sin\frac{\pi}{4}\right)=-2\cos\left(x+\frac{\pi}{4}\right)
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