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

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

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tan^2(θ)=2sec(θ)-1

tan^{2} (θ) = 2 sec (θ) - 1

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

Solution steps

tan^{2} (θ) = 2 sec (θ) - 1

Subtract

2 sec (θ) - 1

from both sides

tan^{2} (θ) - 2 sec (θ) + 1 = 0

Rewrite using trig identities

sec^{2} (θ) - 2 sec (θ) = 0

Solve by substitution

sec (θ) = 2, sec (θ) = 0

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

sec (θ) = 0 :

No Solution

Combine all the solutions

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

5 cosh (x) - 3 sinh (x) = 5

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

sin (2 θ) = \frac{3}{2}, 0 \leq θ \leq 2 π

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

\frac{sin ( x )}{sin ( 2 x )} = \frac{1}{2}

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