What is the general solution for tan^2(x)+4tan(x)=3 ?

The general solution for tan^2(x)+4tan(x)=3 is x=0.57338…+pin,x=-1.35878…+pin

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tan^2(x)+4tan(x)=3

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

x = 0.57338 \dots + πn, x = - 1.35878 \dots + πn

Solution steps

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

Solve by substitution

tan (x) = - 2 + 7, tan (x) = - 2 - 7

tan (x) = - 2 + 7 : x = arctan (- 2 + 7) + πn

tan (x) = - 2 - 7 : x = arctan (- 2 - 7) + πn

Combine all the solutions

x = arctan (- 2 + 7) + πn, x = arctan (- 2 - 7) + πn

Show solutions in decimal form

x = 0.57338 \dots + πn, x = - 1.35878 \dots + πn

sin (1 - 2 x) = 1

4 sin (4 x) = 0

5 cos (x) + 2 = cos (x)

2 tan (4 x) + 1 = 3 tan (4 x)

sec (x) = - 5, π < x < \frac{3 π}{2}

What is the general solution for tan^2(x)+4tan(x)=3 ?
The general solution for tan^2(x)+4tan(x)=3 is x=0.57338…+pin,x=-1.35878…+pin