prove the identity?

0 ⤊

prove the identity:

2cot2x + tanx = cotx

could you please explain each step..cheers.

2007-11-11 05:07:39 · 2 answers · asked by clueless 1 in Science & Mathematics ➔ Mathematics

2 answers

2cot2x + tanx = cotx

Since
cot (2x) = (cot(x) - tan(x))/2

Therefore substituting back
= 2 ((cot(x) - tan(x))/2) + tan(x)
= cot(x) - tan(x) + tan(x)
= cot (x) <<< answer

2007-11-11 05:33:02 · answer #1 · answered by Shh! Be vewy, vewy quiet 6 · 0⤊ 0⤋

2cot2x + tanx
= 2[(1-tan^2(x))/(2tan(x))] + tanx
= [(1-tan^2(x) + tan^2(x)]/(tan(x))]
= 1/tan(x)
= cot(x)

2007-11-11 13:17:29 · answer #2 · answered by sahsjing 7 · 0⤊ 0⤋