Trigonometry

Simplify each expression using the fundamental identities.
1. Sec x csc x / sec^2x+csc^2x
2. Sec x + tan x / sec x + tan x - cos x

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  1. sin^2+cos^2 = 1, so

    sec^2 + csc^2 = 1/cos^2 + 1/sin^2
    = (sin^2+cos^2)/(sin^2 cos^2)
    = 1/(sin^2 cos^2)
    = sec^2 csc^2
    so,

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

    #2 is missing too many parentheses to work on it. That dangling cos x bothers me.

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    posted by Steve

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