Question

Verify the following identity :
cotx – tanx x = [(4 cos ^(2)x – 2) / (sin 2x) ]

Answer 1

@Meepi can we discuss the question???

Answer 2

sure

Answer 3

oh okay.....

Answer 4

i started out like this, but i am stuck!
starting with the LEFT HAND SIDE,
\[\frac{ 4\cos^2 x - 2 }{ \sin 2x }\]
\[\frac{ 2 (2\cos ^2 x - 1) }{ 2\cos x \sin x }\]
\[\frac{ \cos^2 x - 1 }{ \cos x \sin x }\]

Answer 5

I have the same thing lol

Answer 6

i made a mistake.....for the 3rd step, it is supposed to be
\[\frac{ 2\cos^2 x- 1 }{ \cos x \sin x }\]

Answer 7

what about if we simplify (2cos^2x - 1) to cos 2x?

Answer 8

i thought of doing that but won't it make it more complicated??

Answer 9

yeah your right

Answer 10

i think that would work.....hold on...i am trying something

Answer 11

alright thanks :)

Answer 12

\[\frac{ \cos 2x }{ \cos x \sin x }\]
\[\frac{ \cos^2x-\sin^2x }{ \cos x \sin x }\]
\[\frac{ \cos^2x }{ \cos x \sin x } - \frac{ \sin^2 x }{ \cos x \sin x }\]

Answer 13

do you get what i am trying to do??

Answer 14

and can you continue from there??

Answer 15

yeah I get what your trying to do

Answer 16

I got it!!!

Answer 17

yh.....good!

Answer 18

lol

Answer 19

do u need for me to show u what I did?

Answer 20

thanks for your help

Answer 21

okay...sure
you are welcome...

Answer 22

cos ^ 2x / ( cos x sin x ) - (sin ^2x / (cosx sin x )) thats what your wrote but if u look carefully they cancel out.. u end up with ( cosx / sin x) - (sin x/ cos x) = cot x - tan x

Answer 23

yh.....that is it!....(:

Answer 24

awesome thank u!

Answer 25

you are welcome!....