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

(cot (θ) - 3) (2 sin (θ) + 1) = 0

5 sin (θ) - 4 = 0

x, cos (x) + cos (x + y) = 0

cosh (x) = 1

- 2 sin (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