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

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

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tan^2(θ)-4sec(θ)=-5

tan^{2} (θ) - 4 sec (θ) = - 5

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

Solution steps

tan^{2} (θ) - 4 sec (θ) = - 5

Subtract

- 5

from both sides

tan^{2} (θ) - 4 sec (θ) + 5 = 0

Rewrite using trig identities

4 + sec^{2} (θ) - 4 sec (θ) = 0

Solve by substitution

sec (θ) = 2

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

Combine all the solutions

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

tan (θ) = \frac{5}{6}

sin (3 x) cos (2 x) + cos (3 x) sin (2 x) = 1

tan^{2} (θ) + 4 tan (θ) = 3

3 cot (θ) + 7 = 0

sin^{2} (x) - 4 sin (x) = 0

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