Question

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

Answer 1

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

Answer 2

Thank u, helped a lot!☺