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

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

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

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

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

Solution steps

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

Subtract

4 tan (x) - 2

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

tan (x) = 3 : x = arctan (3) + πn

tan (x) = 1 : x = \frac{π}{4} + πn

Combine all the solutions

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

Show solutions in decimal form

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

sin (x) = 2 sin (x) cos (x)

4 sin^{3} (x) + 2 sin^{2} (x) - 2 sin (x) - 1 = 0

3 tan^{2} (θ) = 7 sec (θ) - 5

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

cos (θ) = \frac{2}{3}

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