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March 26, 2017

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(tan/(1+sec)) + ((1+sec)/tan) = 2csc
(Show all work please.)

  • Pre-cal/Trig - ,

    I see tangents and secants on the left side, so I suspect to use the identity
    tan^2x + 1 = sec^2x

    LS
    = tanx(1+secx) + (1+secx)/tanx
    = (tan^2x + 1 + 2secx + sec^2x)/(tanx(1+secx))
    = (sec^2x + 2secx + sec^2x)/(tanx(1+secx))
    = (2sec^2x + 2secx)/(tanx(1+secx))
    = 2secx(secx + 1)/(tanx(1+secx))
    = 2secx/tanx
    = (2/cosx)÷(sinx/cosx)
    = (2/cosx)(cosx/sinx)
    = 2/sinx
    = 2cscx
    = RS

    Q.E.D.

  • Pre-cal/Trig - ,

    y=2sec(1/3x)

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