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Verify that tan^2(x)+6=sec^2(x)+5

  • Math - ,

    Rewrite equation:

    tan^2(x)+6=sec^2(x)+5

    6-5=sec^2(x)tan^2(x)

    sec^2(x)-tan^2(x)=1

    Now you must verify that:

    sec^2(x)-tan^2(x)=1

    tan(x)=sin(x)/cos(x)

    tan(x)=sin(x)*sec(x)

    tan^2(x)=sin^2(x)*sec^2(x)

    sec^2(x)-tan^2(x)=
    sec^2(x)-sin^2(x)*sec^2(x)=
    sec^2(x)*[1-sin^2(x)]

    sin^2(x)+cos^2(x)=1

    cos^2(x)=1-sin^2(x)

    sec^2(x)*[1-sin^2(x)]=
    sec^2(x)*cos^2(x)

    sec(x)=1/cos(x)

    sec^2(x)=1/cos^2(x)

    sec^2(x)*cos^2(x)=
    [1/cos^2(x)]*cos^2(x)=1

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