What is the general solution for tan^2(x)-3sec(x)=-3 ?

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

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tan^2(x)-3sec(x)=-3

tan^{2} (x) - 3 sec (x) = - 3

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

Solution steps

tan^{2} (x) - 3 sec (x) = - 3

Subtract

- 3

from both sides

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

Rewrite using trig identities

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

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 = 2 πn

Combine all the solutions

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

2 sin (\frac{1}{2} x) - 2 = 0

11 sin (b) - 1 = 3 sin (b) - 1

tan^{2} (x) - 5 tan (x) + 6 = 0

3 tan (\frac{x}{4}) - 3 = 0

sin^{2} (3 x) = 1

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