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

The general solution for tan^2(θ)-2sec(θ)=2 is θ=1.23095…+2pin,θ=2pi-1.23095…+2pin,θ=pi+2pin

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tan^2(θ)-2sec(θ)=2

tan^{2} (θ) - 2 sec (θ) = 2

θ = 1.23095 \dots + 2 πn, θ = 2 π - 1.23095 \dots + 2 πn, θ = π + 2 πn

Solution steps

tan^{2} (θ) - 2 sec (θ) = 2

Subtract

2

from both sides

tan^{2} (θ) - 2 sec (θ) - 2 = 0

Rewrite using trig identities

- 3 + sec^{2} (θ) - 2 sec (θ) = 0

Solve by substitution

sec (θ) = 3, sec (θ) = - 1

sec (θ) = 3 : θ = arcsec (3) + 2 πn, θ = 2 π - arcsec (3) + 2 πn

sec (θ) = - 1 : θ = π + 2 πn

Combine all the solutions

θ = arcsec (3) + 2 πn, θ = 2 π - arcsec (3) + 2 πn, θ = π + 2 πn

Show solutions in decimal form

θ = 1.23095 \dots + 2 πn, θ = 2 π - 1.23095 \dots + 2 πn, θ = π + 2 πn

- sin (B) - 4 = 3 sin (B) - 5

cos^{2} (x) - 7 cos (x) - 1 = 0

sec^{2} (x) + tan (x) - 1 = 0

0 = sin (θ)

6 tan^{4} (x) - tan^{2} (x) - 2 = 0

What is the general solution for tan^2(θ)-2sec(θ)=2 ?
The general solution for tan^2(θ)-2sec(θ)=2 is θ=1.23095…+2pin,θ=2pi-1.23095…+2pin,θ=pi+2pin