Question

One complicated trig identity, Someone help!
(tan x) / (sin x- cos x) = (sin^2 x + (sin x)(cos x))/ (cos x - 2 cos ^3 x)

Answer 1

LHS:

sin
---
cos
-------
sin - cos
----
1

flip the bottom over and multiply to get...

Answer 2

sin
--------- = RHS
cos(sin-cos)

RHS:

(sin^2 x + (sin x)(cos x))/ (cos x - 2 cos ^3 x)

sin(sin + cos)
-------------
cos(1 - 2cos^2)

Answer 3

1 sin + cos
tan ------- = tan --------
(sin - cos) 1 - 2cos^2

divide both sides by tan:......

Answer 4

multiply both side by (-1) to get:

-1 sin + cos
------- = ---------
sin-cos 2cos^2 -1

Answer 5

cross multiply....im sure :)

2cos^2 -1 = 2(sin+cos)

Answer 6

2 cos^2 -sin^2 -cos^2 = 2(sin + cos)

cos ^2 - sin^2 = 2(sin+cos)....

Answer 7

sin+cos(sin - cos) = sin^2 - cos^2 NOT (2)sin+cos

Answer 8

go back to the cross multiply...

Answer 9

Thank you for showing me, but unfortunately I'm required to work on one side

Answer 10

if you can work it out to meet in the middle, then you simply reverse it to get back to the one side....

How you solve it really doesnt matter a hilll of beans :)

Answer 11

ok, thanks :)

Answer 12

but let me show you that it DOES work out :)

I gots:

-(2cos^2 -1) = sin^2 - cos^2

-(2cos^2 -(sin^2 + cos^2)) = sin^2 - cos^2

-(2cos^2 -sin^2 -cos^2) = sin^2 - cos^2

-(cos^2 - sin^2) = sin^2 - cos^2
sin^2 - cos^2 = sin^2 - cos^2 (proofed)

Answer 13

I'm kinda confused now...

Answer 14

who requires you ta work only one side?

Answer 15

my professor requires us to work one side to equal other side

Answer 16

since both sides are equally "messed up"; it would be best to "simplify" both sides till they are equal. I you can only work with one die, you are pretty much tieing your hands behind your back.....

Answer 17

my keyboard hates me :)

Answer 18

ok, its fine lol.. i appreciate the help, it would be easier to work both sides.. wish i could