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

- 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

- 1 = tan (θ)

4 cos (x) = 2

5 + 2 tan (3 θ + \frac{π}{3}) = 3

3 sec^{2} (x) - 6 = 0, 0 \leq x \leq 2 π

cot^{2} (x) = 1

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