What is the general solution for 6sec^2(x)-6sec(x)=12 ?

The general solution for 6sec^2(x)-6sec(x)=12 is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin

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6sec^2(x)-6sec(x)=12

6 sec^{2} (x) - 6 sec (x) = 12

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

Solution steps

6 sec^{2} (x) - 6 sec (x) = 12

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 (a) = \frac{2}{2}

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

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

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

cos (x) = 9

What is the general solution for 6sec^2(x)-6sec(x)=12 ?
The general solution for 6sec^2(x)-6sec(x)=12 is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin