What is the general solution for tan^2(θ)-sec(θ)=1 ?

The general solution for tan^2(θ)-sec(θ)=1 is θ= pi/3+2pin,θ=(5pi)/3+2pin,θ=pi+2pin

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tan^2(θ)-sec(θ)=1

tan^{2} (θ) - sec (θ) = 1

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

Solution steps

tan^{2} (θ) - sec (θ) = 1

Subtract

1

from both sides

tan^{2} (θ) - sec (θ) - 1 = 0

Rewrite using trig identities

- 2 - sec (θ) + sec^{2} (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 = π + 2 πn

Combine all the solutions

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

sin (x) = \frac{8}{10}

sin (x) cos (2 x) + cos (x) sin (2 x) = 0

7 cos (5 x) + 9 = 12

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

3 cot (2 x) = - 1

What is the general solution for tan^2(θ)-sec(θ)=1 ?
The general solution for tan^2(θ)-sec(θ)=1 is θ= pi/3+2pin,θ=(5pi)/3+2pin,θ=pi+2pin