Trigonometry

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How do you verify the equation is an identity?
Tan^2x-tan^2y=sec^2x-sec^2y

and, how do you factor and simplify,
cscx(sin^2x+cos^2xtanx)/sinx+cosx

  • Trigonometry -

    One of the basic identities is
    tan^2 A + 1 = sec^2 A which gives Tan^2 A = sec^2 A - 1

    so
    Left side
    = tan^2x-tan^2y
    = sec^2x - 1 -(sec^2y - 1)
    = sec^2x - sec^2y
    = Right Side

  • Trigonometry -

    For the second, I will assume you meant

    cscx(sin^2x+cos^2xtanx)/(sinx+cosx)
    = 1/sinx(sin^2x + cos^2xsinx/cosx)/(sinx + cosx)
    = 1/sinx(sin^2x + sinxcosx)/(sinx+cosx)
    = (sinx + cosx)/sinx + cosx)
    = 1

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