verify the identity : ln cot x = - ln tan x?

1 ⤊

verify the identity : ln cot x = - ln tan x?

2007-09-28 08:51:12 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

4 answers

cot x = 1/tan x
ln cot x = ln 1/tanx=ln1 -ln tanx
ln 1=0
so, ln cot x = -ln tan x

2007-09-28 08:55:00 · answer #1 · answered by cidyah 7 · 1⤊ 0⤋

ln cotx = ln 1/tanx = ln 1 - ln tanx = 0 - ln tanx = - ln tanx

2007-09-28 15:55:52 · answer #2 · answered by Swamy 7 · 0⤊ 0⤋

ln cotx = ln(1/tanx)

ln(1/tanx) = ln 1 - ln tanx because ln(a/b) = ln a - ln b

but ln 1 = 0

so ln(1/tan x) = 0 - ln tanx

= - ln tanx

so ln cotx = - ln tan x

2007-09-28 16:16:00 · answer #3 · answered by mohanrao d 7 · 0⤊ 0⤋

Yes its true because..........

ln cotx=ln 1/tanx
=ln [(tanx)^(-1)]
=(-1) ln tanx
= - ln tanx

2007-09-28 16:01:52 · answer #4 · answered by prats 2 · 0⤊ 0⤋