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Math Help - Proving an identity

  1. #1
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    Proving an identity

    Having some trouble proving this identity.

     cosx+ sinxtanx= \frac {1}{cosx}

    This is where I keep getting stuck.

    R.S=\frac {1}{cosx}
    L.S= cosx+ sinx\frac {sinx}{cosx}
    =cosx + \frac {sin^2x}{cosx}

    =\frac {1 + sin^2x}{cosx}

    Help please.

    Thanks in advance.

    Sincerely,

    Raymond
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    Re: Proving an identity

    \cos x + \frac{\sin^2 x}{\cos x} \neq \frac{1+\sin^2x}{\cos x} . You're not putting these under a common denominator properly.
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  3. #3
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    Re: Proving an identity

    Quote Originally Posted by Bruno J. View Post
    \cos x + \frac{\sin^2 x}{\cos x} \neq \frac{+\sin^2x}{\cos x} . You're not putting these under a common denominator properly.
    Is it...
    \cos x + \frac{\sin^2 x}{\cos x} = \frac{cosx+\sin^2x}{\cos x} ?
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  4. #4
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    Re: Proving an identity

    Wait, i think I get it. Hold on.
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  5. #5
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    Re: Proving an identity

     cosx+ sinxtanx= \frac {1}{cosx}

    R.S=\frac {1}{cosx}

    L.S=\frac {cos x}{1} + \frac{\sin^2 x}{\cos x} = \frac{cos^2x}{cos x}+\frac {sin^2x}{cosx} = \frac {sin^2x+cos^2x}{cosx}

    = \frac {1}{cosx}; R.S=L.S

    Correct now?
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  6. #6
    MHF Contributor Siron's Avatar
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    Re: Proving an identity

    Correct!
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