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=(2pi)/3+2pin,x=(4pi)/3+2pin

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

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

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Solution steps

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

Solve by substitution

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

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

No Solution

sec (x) = - 2 : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Combine all the solutions

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

- 4 arctan (x) = π

sin^{2} (x) = sin (x) cos (x)

sin (x) = - \frac{3}{2}, 0 \leq x \leq 2 π

sin^{2} (x) = 1 + cos^{2} (x)

cos^{2} (θ) = 0

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=(2pi)/3+2pin,x=(4pi)/3+2pin