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

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

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tan^2(θ)-3sec(θ)=-3

tan^{2} (θ) - 3 sec (θ) = - 3

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

Solution steps

tan^{2} (θ) - 3 sec (θ) = - 3

Subtract

- 3

from both sides

tan^{2} (θ) - 3 sec (θ) + 3 = 0

Rewrite using trig identities

2 + sec^{2} (θ) - 3 sec (θ) = 0

Solve by substitution

sec (θ) = 2, sec (θ) = 1

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

sec (θ) = 1 : θ = 2 πn

Combine all the solutions

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

arctan (\frac{w}{2}) + arctan (\frac{w}{4}) + arctan (\frac{w}{6}) = 18 0^{\circ}

sin (x + \frac{π}{6}) = 0

7 sin (x) + 3 = sin (x) + 2

24 cos (x) = 122

cos (3 x) = \frac{3}{3}

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