Posted by **Denise** on Sunday, July 24, 2011 at 5:28pm.

Find all solutions in the interval [0, pi], 2sec^2x+tan^2x-3=0

- pre cal 2 -
**Reiny**, Sunday, July 24, 2011 at 6:26pm
2sec^2x+tan^2x-3=0

2/cos^2x + sin^2x/cos^2x - 3 = 0

multiply by cos^2x

2 + sin^2x - 3cos^2x = 0

2 + (1 - cos^2x) - 3cos^2x = 0

3 = 4 cos^2x

cos^2 = 3/4

cosx = ± √3/2

x = 30° , 150° , 210° , or 330°

x = π/6, 5π/6 , 7π/6, or 11π/6

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