SOLUTION: Solve the equation for 0≤x≤2pi. Write your answer as a multiple of pi, if possible. (tan^2)x = {{{(-3/2)}}} secx Thanks!

Algebra ->  Trigonometry-basics -> SOLUTION: Solve the equation for 0≤x≤2pi. Write your answer as a multiple of pi, if possible. (tan^2)x = {{{(-3/2)}}} secx Thanks!      Log On


   

Question 1082640: Solve the equation for 0≤x≤2pi. Write your answer as a multiple of pi, if possible.

(tan^2)x = %28-3%2F2%29 secx

Thanks!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
(tan^2)x = %28-3%2F2%29 secx
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tan%5E2%28x%29+=+-3sec%28x%29%2F2%29
Multiply thru by cos(x)
tan*sin = -3/2
sin^2/cos = -3/2
sin^2 = -3cos/2
1-cos^2 = -3cos/2
2 - 2cos^2 = -3cos
2cos^2 - 3cos - 2 = 0
(2cos + 1)*(cos - 2) = 0
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cos = 2 --> no real number solution
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2cos + 1 = 0
cos = -1/2
etc