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

The general solution for 2tan(θ)+sec^2(θ)=4 is θ= pi/4+pin,θ=-1.24904…+pin

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2tan(θ)+sec^2(θ)=4

2 tan (θ) + sec^{2} (θ) = 4

θ = \frac{π}{4} + πn, θ = - 1.24904 \dots + πn

Solution steps

2 tan (θ) + sec^{2} (θ) = 4

Subtract

4

from both sides

2 tan (θ) + sec^{2} (θ) - 4 = 0

Rewrite using trig identities

- 3 + tan^{2} (θ) + 2 tan (θ) = 0

Solve by substitution

tan (θ) = 1, tan (θ) = - 3

tan (θ) = 1 : θ = \frac{π}{4} + πn

tan (θ) = - 3 : θ = arctan (- 3) + πn

Combine all the solutions

θ = \frac{π}{4} + πn, θ = arctan (- 3) + πn

Show solutions in decimal form

θ = \frac{π}{4} + πn, θ = - 1.24904 \dots + πn

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

csc (x) = 7

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

sin (2 θ) - cos (θ) - 2 sin (θ) + 1 = 0

2 cos (x) + 1 = 0 - 2, π \leq x \leq 2 π

What is the general solution for 2tan(θ)+sec^2(θ)=4 ?
The general solution for 2tan(θ)+sec^2(θ)=4 is θ= pi/4+pin,θ=-1.24904…+pin