solve for all 0≤x≤2π

Question

1.   2tan²x-3sec x+3=0
2.   cot x-√3=csc x

Answer 1

2tan²x - 3secx + 3 = 0

2(sec²x - 1) - 3secx + 3 = 0

2sec²x - 3secx + 1 = 0

(2secx - 1)(secx - 1) = 0

secx = 1/2 or secx = 1

So, cosx = 2 or cosx = 1

The equation cosx = 2 has no solution. cosx = 1 when x = 0 or 2π

Answer 2

1) Multiply both sides by cos² x

2) Multiply both sides by sin x