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Math Help - verifying trig identity

  1. #1
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    verifying trig identity

    sin3x/sinx-cos3x/cosx=2
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Ok using substitution

    Quote Originally Posted by Thelema View Post
    sin3x/sinx-cos3x/cosx=2
    we have \frac{3sin(x)-4sin(x)^3}{sin(x)}-\frac{cos(x)^3-3cos(x)sin(x)^2}{cos(x)}=2 can you seehwere to go from there?
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  3. #3
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    Hello, Thelema!

    \frac{\sin3x}{\sin x}-\frac{\cos3x}{\cos x}\;=\;2

    Combine the fractions: . \frac{\sin3x}{\sin x}\!\cdot\!{\color{blue}\frac{\cos x}{\cos x}} - \frac{\cos3x}{\cos x}\!\cdot\!{\color{blue}\frac{\sin x}{\sin x}} \;=\;\frac{\sin3x\cos x - \cos3x\sin x}{\sin x\cos x}

    . . =\;\frac{\sin(3x-x)}{\sin x\cos x} \;=\;\frac{\sin2x}{\sin x\cos x} \;=\;\frac{2\sin x\cos x}{\sin x\cos x} \;=\;2

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