Pre-calc

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Verify this identity. How would you prove it

(sin^3(x)+cos^3(x))÷(1-2cos^2(x)) = (sec(x)-sin(x))÷(tan(x)-1)

  • Pre-calc -

    on the LS,

    sin^3+cos^3 = (sin+cos)(sin^2 - sin*cos + cos^2) = (sin+cos)(1-sin*cos)
    1-2cos^2 = sin^2-cos^2 = (sin+cos)(sin-cos)

    divide, giving (1-sin*cos)/(sin-cos)

    on the RS,

    sec-sin = 1/cos - sin = (1-sin*cos)/cos
    tan-1 = sin/cos - 1 = (sin-cos)/cos

    divide, giving (1-sin*cos)/(sin-cos)

    LS = RS

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