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Posted by on Tuesday, May 31, 2011 at 9:20pm.

How do I prove the following Identity?

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

If there is a certain website or suggestion to help with these type of equations I would greatly appreciate it. I've been studying these for a while but still get pretty confused.

  • Trig - , Tuesday, May 31, 2011 at 10:35pm

    sec(x)*[sec(x)-cos(x)]=

    sec(x)*sec(x)-sec(x)*cos(x)

    Remark:
    sec(x)=1/cos(x)

    sec(x)*sec(x)-sec(x)*cos(x)=

    1/cos(x) * 1/cos(x) - 1/cos(x) * cos(x)=

    1/cos^2(x)-1=

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

    1-cos^2(x)/cos^2(x)

    Remark:

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

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

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

  • Trig - , Wednesday, June 1, 2011 at 7:12am

    LS = sec x(sec x-cos x)
    = (1/cosx)(1/cosx - cosx)
    = 1/cos^2x - 1
    = sec^2 - 1
    = tan^2x (by definition)
    = RS

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