What is the general solution for 2tan^2(x)-1=3tan(x) ?

The general solution for 2tan^2(x)-1=3tan(x) is x=1.05912…+pin,x=-0.27372…+pin

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2tan^2(x)-1=3tan(x)

2 tan^{2} (x) - 1 = 3 tan (x)

x = 1.05912 \dots + πn, x = - 0.27372 \dots + πn

Solution steps

2 tan^{2} (x) - 1 = 3 tan (x)

Solve by substitution

tan (x) = \frac{3 + 17}{4}, tan (x) = \frac{3 - 17}{4}

tan (x) = \frac{3 + 17}{4} : x = arctan (\frac{3 + 17}{4}) + πn

tan (x) = \frac{3 - 17}{4} : x = arctan (\frac{3 - 17}{4}) + πn

Combine all the solutions

x = arctan (\frac{3 + 17}{4}) + πn, x = arctan (\frac{3 - 17}{4}) + πn

Show solutions in decimal form

x = 1.05912 \dots + πn, x = - 0.27372 \dots + πn

8 csc^{2} (x) - 2 cot (x) = 9

cos (d) = \frac{9}{15}

coth^{2} (x) + csch^{2} (x) = 2

tan (x) = \frac{3}{9}

2 cos (x) = 3 cot (x)

What is the general solution for 2tan^2(x)-1=3tan(x) ?
The general solution for 2tan^2(x)-1=3tan(x) is x=1.05912…+pin,x=-0.27372…+pin