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

The general solution for 2tan^2(x)-5tan(x)+2=0 is x=1.10714…+pin,x=0.46364…+pin

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

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

x = 1.10714 \dots + πn, x = 0.46364 \dots + πn

Solution steps

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

Solve by substitution

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

tan (x) = 2 : x = arctan (2) + πn

tan (x) = \frac{1}{2} : x = arctan (\frac{1}{2}) + πn

Combine all the solutions

x = arctan (2) + πn, x = arctan (\frac{1}{2}) + πn

Show solutions in decimal form

x = 1.10714 \dots + πn, x = 0.46364 \dots + πn

9 sec^{2} (x) - 9 sec (x) = 18

sec^{2} (x) - 8 sec (- x) - 20 = 0

3 arccos (5 x) = 2 π

3 cot (3 θ + \frac{π}{3}) + 1 = 0

tan (θ) = \frac{4}{13}

What is the general solution for 2tan^2(x)-5tan(x)+2=0 ?
The general solution for 2tan^2(x)-5tan(x)+2=0 is x=1.10714…+pin,x=0.46364…+pin