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Math Help - Please send me in the right direction

  1. #1
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    Please send me in the right direction

    Hey, I'm stuck on these problems if anyone could help me it would be amazing!

    tan^2x=3/2secx

    sqrt3 sinx - cosx=sqrt3
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  2. #2
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    Quote Originally Posted by progeek View Post
    Hey, I'm stuck on these problems if anyone could help me it would be amazing!

    tan^2x=3/2secx

    sqrt3 sinx - cosx=sqrt3
    #1 ...

    \tan^2{x} = \sec^2{x} - 1 ... solve the resulting quadratic for \sec{x}


    #2 ...

    \sqrt{3} \cdot \sin{x} = \cos{x} + \sqrt{3}

    square both sides ...

    3\sin^2{x} = \cos^2{x} + 2\sqrt{3} \cdot \cos{x} + 3

    3(1 - \cos^2{x}) = \cos^2{x} + 2\sqrt{3} \cdot \cos{x} + 3

    solve the quadratic for \cos{x}
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  3. #3
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    Quote Originally Posted by skeeter View Post
    #1 ...

    \tan^2{x} = \sec^2{x} - 1 ... solve the resulting quadratic for \sec{x}


    #2 ...

    \sqrt{3} \cdot \sin{x} = \cos{x} + \sqrt{3}

    square both sides ...

    3\sin^2{x} = \cos^2{x} + 2\sqrt{3} \cdot \cos{x} + 3

    3(1 - \cos^2{x}) = \cos^2{x} + 2\sqrt{3} \cdot \cos{x} + 3

    solve the quadratic for \cos{x}

    Thank you so much for the help. I got the second one but I'm still confused on the first problem. I got sec^2x-3/2secx-1. When I factor that out I get (sec-3/2)(sec+2/3) When I solve for both of those I don't get anything that I can redeem as an answer.
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  4. #4
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    Quote Originally Posted by progeek View Post
    Thank you so much for the help. I got the second one but I'm still confused on the first problem. I got sec^2x-3/2secx-1. When I factor that out I get (sec-3/2)(sec+2/3) When I solve for both of those I don't get anything that I can redeem as an answer.
    \sec^2{x} - \frac{3}{2}\sec{x} - 1 = 0

    2\sec^2{x} - 3\sec{x} - 2 = 0

    (2\sec{x} + 1)(\sec{x} - 2) = 0
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  5. #5
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    Quote Originally Posted by skeeter View Post
    \sec^2{x} - \frac{3}{2}\sec{x} - 1 = 0

    2\sec^2{x} - 3\sec{x} - 2 = 0

    (2\sec{x} + 1)(\sec{x} - 2) = 0
    ohhhhhhh, I feel so stupid. Yet at again thank you sooo much!
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