What is the general solution for 2sec^2(x)-3sec(x)-2=0 ?

The general solution for 2sec^2(x)-3sec(x)-2=0 is x= pi/3+2pin,x=(5pi)/3+2pin

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2sec^2(x)-3sec(x)-2=0

2 sec^{2} (x) - 3 sec (x) - 2 = 0

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

2 sec^{2} (x) - 3 sec (x) - 2 = 0

Solve by substitution

sec (x) = 2, sec (x) = - \frac{1}{2}

sec (x) = 2 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sec (x) = - \frac{1}{2} :

No Solution

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

tan (θ) + \frac{1}{3} = 0

12 cos^{2} (x) - 3 = 0

csc^{2} (θ) + 4 csc (θ) - 5 = 0

cos^{2} (x) - cos (x) = 0, 0 \leq x \leq 2 π

\frac{sin ( 2 x )}{cos ( x )} = 2, 0 \leq x \leq π

What is the general solution for 2sec^2(x)-3sec(x)-2=0 ?
The general solution for 2sec^2(x)-3sec(x)-2=0 is x= pi/3+2pin,x=(5pi)/3+2pin