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Math Help - Solving with Trig Identities..

  1. #1
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    Solving with Trig Identities..

    Solve the following equations given that 0 \leq x \leq 2\pi.

     a) \cos^2x - \sin^2x = 1

     b) 1 + \sqrt{3}\tan2x = 0


    Your help is really appreciated. Thanks.
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  2. #2
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     a) \cos^2x - \sin^2x = 1

     b) 1 + \sqrt{3}\tan2x = 0


    Your help is really appreciated. Thanks.[/quote]
    a) Replace sin^2 X by 1-cos^2 X.
    The equation becomes 2cos^2 X =2
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  3. #3
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    Cool

    Quote Originally Posted by Savior_Self View Post
    Solve the following equations given that 0 \leq x \leq 2\pi.

     a) \cos^2x - \sin^2x = 1

     b) 1 + \sqrt{3}\tan2x = 0


    Your help is really appreciated. Thanks.
    b) tan2X = -1/root3
    Then set the range according to 2X. that is From 0<2X<4pi
    then replace 2X by another variable say Y
    tan Y= -1/root3
    solve for Y in the new given range.
    At the end divide the answers by 2, because 2X=Y. Is that Ok.
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