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how would you determine a formula for cot(2x) using only cot(x)? Thenhow would you determine a formula for sec(2x) using only sec(x)?

  • math -

    cot 2x = 1/tan 2x
    = 1/[2tanx/(1-tan^2(x))]
    = (1-tan^2(x))/2tanx
    = [1 - 1/cot^2(x))/(2/cotx)
    = [(cot^2(x) - 1)/cot^2(x)]/[2/cotx]
    = (cot^2(x) - 1)/(2cotx)

    I don't know if that is the simplest way, I just sort of followed by nose.

    you can try sec 2x by noting
    sec 2x = 1/cos 2c
    then using cos2x = 2cos^2(x) - 1

    follow the above procedure.

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