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=(2pi)/3+2pin,x=(4pi)/3+2pin

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

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

x = \frac{2 π}{3} + 2 πn, x = \frac{4 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{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Combine all the solutions

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

tan^{2} (θ) - 6 sec (θ) = 6

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

9 cos^{2} (x) + 18 cos (x) + 9 = 0

cot (3 x) = - \frac{3}{3}

sin (6 θ) = 0

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=(2pi)/3+2pin,x=(4pi)/3+2pin