Posted by kim on .
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,
cot 2x = 1/tan 2x
= 1/[2tanx/(1tan^2(x))]
= (1tan^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.