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

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

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

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

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

Solution steps

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

Solve by substitution

sec (x) = 2, sec (x) = - 1

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

sec (x) = - 1 : x = π + 2 πn

Combine all the solutions

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

sin (x) = \frac{4}{5}

4 sin^{2} (θ) = 3 cos^{2} (θ), 0^{\circ} < θ < 36 0^{\circ}

2 sin (x) - 2 = 0

tan (θ) = \frac{1}{2}

sin^{2} (x) + cos (x) + 1 = 0

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