What is the general solution for tan^2(x)-4sec(x)+5=0 ?

The general solution for tan^2(x)-4sec(x)+5=0 is x= pi/3+2pin,x=(5pi)/3+2pin

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tan^2(x)-4sec(x)+5=0

tan^{2} (x) - 4 sec (x) + 5 = 0

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

Solution steps

tan^{2} (x) - 4 sec (x) + 5 = 0

Rewrite using trig identities

4 + sec^{2} (x) - 4 sec (x) = 0

Solve by substitution

sec (x) = 2

sec (x) = 2 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

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

cot (θ) = \frac{3}{4}

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

tan (x) = \frac{7}{3}

3 = 3 cos (2 θ) + sin (2 θ)

8 sin^{2} (x) = sin (x)

What is the general solution for tan^2(x)-4sec(x)+5=0 ?
The general solution for tan^2(x)-4sec(x)+5=0 is x= pi/3+2pin,x=(5pi)/3+2pin