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

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

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sec^2(θ)=2tan(θ)

sec^{2} (θ) = 2 tan (θ)

θ = \frac{π}{4} + πn

Solution steps

sec^{2} (θ) = 2 tan (θ)

Subtract

2 tan (θ)

from both sides

sec^{2} (θ) - 2 tan (θ) = 0

Rewrite using trig identities

1 + tan^{2} (θ) - 2 tan (θ) = 0

Solve by substitution

tan (θ) = 1

tan (θ) = 1 : θ = \frac{π}{4} + πn

Combine all the solutions

θ = \frac{π}{4} + πn

2 sin (2 x) + 2 = 0

2 cos^{2} (θ) - 3 sin (θ) + 2 = 0

sin (x) + sin (2 x) + sin (3 x) = 0

sin^{2} (x) - cos^{2} (x) = 1 + cos (x)

36 cos^{2} (x) - 9 = 0

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