how to prove that COS ²X - 2 COS X -2 = 0 ?
2007-10-25 19:48:21 · 4 answers · asked by Gary 1 in Science & Mathematics ➔ Mathematics
the goal is to prove that the equation on the left is equal to zero.
The left equation is
cos ²x - 2cosx - 2
need to show the steps to prove that it is equal to zero
2007-10-25 19:57:59 · update #1
It's been a long time since I worked these problems. This solution may/may not work. If it does, great! If not, apologies.
Let y = cos x
Then your equation becomes y^2 - 2y - 2 = 0
Use the quadratic formula to solve for y.
This yields y = 1 +/- sq rt 3
substitute back cosx for y
cos x = 1 +/- sqrt 3
cos x = 1 + 1.732 and 1 - 1.732
since cos x cannot be greater than 1, you may disregard the first solution
cos x = -.732
x = about 133 deg or 223 deg since cos x is negative in 2nd and 3rd quadrants.
2007-10-26 01:20:23 · answer #1 · answered by duffy 4 · 0⤊ 1⤋
It doesn't work for x = 0.
cos(0) = 1
so cos²(0) - 2 cos(0) - 2 = 1 -2 -2 = -3
2007-10-26 03:30:30 · answer #2 · answered by Demiurge42 7 · 0⤊ 0⤋
email Steven Hawking
2007-10-26 02:56:44 · answer #3 · answered by Anonymous · 0⤊ 1⤋
2 i dontknow maybe make it clearer
2007-10-26 02:51:38 · answer #4 · answered by KEB 2 · 0⤊ 1⤋