anonymous
  • anonymous
Solving trigonometric equations! Help!
Precalculus
chestercat
  • chestercat
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anonymous
  • anonymous
How did 3(1-cos^2x)+cos^2x = 2 Became: 3 - 2cos^2x=2 ?! Could you guys help me with this one!
anonymous
  • anonymous
Why didnt we multiple 3 by (1 - cos^2x) as a whole? Thanks!
campbell_st
  • campbell_st
you need to solve for x so start with \[1 - \cos^2(x) = \sin^2(x) \] and substituting will give \[3\sin^2(x) + \cos^2(x) = 2\] or \[2 \sin^2(x) + \sin^2(x) + \cos^2(x) = 1\] and \[\sin^2(x) + \cos^2(x) = 1\] so you have \[2 \sin^2(x) + 1 = 2\] or \[2\sin^2(x) = 1\] you should be able to solve for x now in my solution I've tried to show every step so you can follow it... there are quicker solutions...

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