What is the general solution for tan^2(x)-3sec(x)+3=0 ?

The general solution for tan^2(x)-3sec(x)+3=0 is x= pi/3+2pin,x=(5pi)/3+2pin,x=2pin

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

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

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 = 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

cos (5 t) cos (2 t) = - sin (5 t) sin (2 t)

x, cos (x) = sin (y)

tan (θ) = \frac{5}{8}

3 cos^{2} (x) = 9 sin (x) + 9

cos^{2} (x) - 2 cos (x) = 3

What is the general solution for tan^2(x)-3sec(x)+3=0 ?
The general solution for tan^2(x)-3sec(x)+3=0 is x= pi/3+2pin,x=(5pi)/3+2pin,x=2pin