What is the general solution for 3tan^2(x)-5tan(x)+2=0 ?

The general solution for 3tan^2(x)-5tan(x)+2=0 is x= pi/4+pin,x=0.58800…+pin

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3tan^2(x)-5tan(x)+2=0

3 tan^{2} (x) - 5 tan (x) + 2 = 0

x = \frac{π}{4} + πn, x = 0.58800 \dots + πn

Solution steps

3 tan^{2} (x) - 5 tan (x) + 2 = 0

Solve by substitution

tan (x) = 1, tan (x) = \frac{2}{3}

tan (x) = 1 : x = \frac{π}{4} + πn

tan (x) = \frac{2}{3} : x = arctan (\frac{2}{3}) + πn

Combine all the solutions

x = \frac{π}{4} + πn, x = arctan (\frac{2}{3}) + πn

Show solutions in decimal form

x = \frac{π}{4} + πn, x = 0.58800 \dots + πn

θ, ρ = (4 sin (φ) cos (θ))

sin^{2} (a) - cos^{2} (a) = 1

arcsin (x) = - 1

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

3 \cdot tan^{2} (x) = 1

What is the general solution for 3tan^2(x)-5tan(x)+2=0 ?
The general solution for 3tan^2(x)-5tan(x)+2=0 is x= pi/4+pin,x=0.58800…+pin