anonymous
  • anonymous
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)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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amistre64
  • amistre64
LHS: sin --- cos ------- sin - cos ---- 1 flip the bottom over and multiply to get...
amistre64
  • amistre64
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)
amistre64
  • amistre64
1 sin + cos tan ------- = tan -------- (sin - cos) 1 - 2cos^2 divide both sides by tan:......

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amistre64
  • amistre64
multiply both side by (-1) to get: -1 sin + cos ------- = --------- sin-cos 2cos^2 -1
amistre64
  • amistre64
cross multiply....im sure :) 2cos^2 -1 = 2(sin+cos)
amistre64
  • amistre64
2 cos^2 -sin^2 -cos^2 = 2(sin + cos) cos ^2 - sin^2 = 2(sin+cos)....
amistre64
  • amistre64
sin+cos(sin - cos) = sin^2 - cos^2 NOT (2)sin+cos
amistre64
  • amistre64
go back to the cross multiply...
anonymous
  • anonymous
Thank you for showing me, but unfortunately I'm required to work on one side
amistre64
  • amistre64
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 :)
anonymous
  • anonymous
ok, thanks :)
amistre64
  • amistre64
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)
anonymous
  • anonymous
I'm kinda confused now...
amistre64
  • amistre64
who requires you ta work only one side?
anonymous
  • anonymous
my professor requires us to work one side to equal other side
amistre64
  • amistre64
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.....
amistre64
  • amistre64
my keyboard hates me :)
anonymous
  • anonymous
ok, its fine lol.. i appreciate the help, it would be easier to work both sides.. wish i could

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