SOLUTION: Hello, can you please help me prove that 3cos^2x-2cosx=0? Thank you very much.

Algebra ->  Trigonometry-basics -> SOLUTION: Hello, can you please help me prove that 3cos^2x-2cosx=0? Thank you very much.      Log On


   

Question 260365: Hello, can you please help me prove that 3cos^2x-2cosx=0? Thank you very much.
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, think of this as regular factoring steps.
3%2Acos%5E2%28x%29-2%2Acos%28x%29=0
step 1 - factor out a cos(x) to get
cos%28x%29%2A%283cos%28x%29+-+2%29=+0
step 2 -set each part = 0 and solve for x. We get
cos(x) = 0
x = pi/2, or 3pi/2
3cos(x) -2 = 0
cos(x) = 2/3
we estimate this as 48.1 degrees
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so we have 48.1, 90, and 270 degrees
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since this is not an identity, we can't "prove" for all x.