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Math Help - Trig Identity Proof

  1. #1
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    Trig Identity Proof

    Hi,

    I've been playing around with this thing for hours trying to get it to work and have made no progress ;\. anyone know how to do this?

    Prove that for all angles θ,

    tan(θ)^2/sin(θ)^2=1+tan(θ)^2

    any help would be much appreciated,

    thanks,

    Coukapecker
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Trig Identity Proof

    Write (I use x in stead of \theta for a moment):
    \tan^2(x)=\frac{\sin^2(x)}{\cos^2(x)}
    And also write:
    1+\tan^2(x)=1+\frac{\sin^2(x)}{\cos^2(x)} =\frac{\cos^2(x)+\sin^2(x)}{\cos^2(x)}= \frac{1}{\cos^2(x)}

    Try to continue with this.
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  3. #3
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    Re: Trig Identity Proof

    That's actually where I got to without assistance, but I can't figure out what to do after


    tan^2(x)/sin^2(x)=sec^2(x)
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: Trig Identity Proof

    You have everything to prove the identity:
    LHS:
    \frac{\frac{\sin^2(x)}{\cos^2(x)}}{\sin^2(x)}= \frac{\sin^2(x)}{\cos^2(x)}\cdot \frac{1}{\sin^2(x)}=\frac{1}{\cos^2(x)}

    RHS:
    1+\tan^2(x)=\frac{1}{\cos^2(x)}

    So LHS=RHS
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  5. #5
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    Re: Trig Identity Proof

    Man,

    I've bee staring at (sin(x))^2/(cos(x))^2/(sin(x))^2) for like hours. Somehow managed to convince myself that you couldn't work with it.

    Thanks for that :P.
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  6. #6
    MHF Contributor Siron's Avatar
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    Re: Trig Identity Proof

    You're welcome! Also in trigonometry you still have to know the important algebraic rules .
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