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

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

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2tan(θ)=sec^2(θ)

2 tan (θ) = sec^{2} (θ)

θ = \frac{π}{4} + πn

Solution steps

2 tan (θ) = sec^{2} (θ)

Subtract

sec^{2} (θ)

from both sides

2 tan (θ) - sec^{2} (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

tan (θ) = \frac{14}{15}

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

sin (- θ) = - \frac{3}{5}, tan (θ) > 0

tan^{3} (x) + tan^{2} (x) - 3 tan (x) - 3 = 0

tan^{2} (x) + 5 = 3 sec^{2} (x)

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