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

The general solution for sec^2(x)=2tan(x)+4 is x=1.24904…+pin,x=(3pi)/4+pin

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sec^2(x)=2tan(x)+4

sec^{2} (x) = 2 tan (x) + 4

x = 1.24904 \dots + πn, x = \frac{3 π}{4} + πn

Solution steps

sec^{2} (x) = 2 tan (x) + 4

Subtract

2 tan (x) + 4

from both sides

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

Rewrite using trig identities

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

Solve by substitution

tan (x) = 3, tan (x) = - 1

tan (x) = 3 : x = arctan (3) + πn

tan (x) = - 1 : x = \frac{3 π}{4} + πn

Combine all the solutions

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

Show solutions in decimal form

x = 1.24904 \dots + πn, x = \frac{3 π}{4} + πn

- 4 cos (θ) = - sin^{2} (θ) + 1

2 sin^{2} (θ) + 3 sin (θ) = 0, 0 \leq θ < 2 π

sin (θ) = \frac{π}{2}

arcsin (\frac{900 x ^{2} - 1}{900 x ^{2} + 1}) = 1.18

sin (b - 2 0^{\circ}) = cos (142. 7^{\circ})

What is the general solution for sec^2(x)=2tan(x)+4 ?
The general solution for sec^2(x)=2tan(x)+4 is x=1.24904…+pin,x=(3pi)/4+pin