Posted by **kim** on Sunday, April 19, 2009 at 6:52pm.

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 -
**Reiny**, Sunday, April 19, 2009 at 7:23pm
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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