What is the general solution for 2sec^2(x)-2sec(x)=4 ?

The general solution for 2sec^2(x)-2sec(x)=4 is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin

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2sec^2(x)-2sec(x)=4

2 sec^{2} (x) - 2 sec (x) = 4

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

Solution steps

2 sec^{2} (x) - 2 sec (x) = 4

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 (2 x) = - sin (4 x)

tan (x) + sin (x) = 0

cos (x) (2 sin (x) + 1) = 0, 0 \leq x \leq 2 π

3 sin (x) - 1 = 2

sin (t) = \frac{1}{2}

What is the general solution for 2sec^2(x)-2sec(x)=4 ?
The general solution for 2sec^2(x)-2sec(x)=4 is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin