What is the general solution for 3tan^2(x)-10tan(x)+7=0 ?

The general solution for 3tan^2(x)-10tan(x)+7=0 is x=1.16590…+pin,x= pi/4+pin

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3tan^2(x)-10tan(x)+7=0

3 tan^{2} (x) - 10 tan (x) + 7 = 0

x = 1.16590 \dots + πn, x = \frac{π}{4} + πn

Solution steps

3 tan^{2} (x) - 10 tan (x) + 7 = 0

Solve by substitution

tan (x) = \frac{7}{3}, tan (x) = 1

tan (x) = \frac{7}{3} : x = arctan (\frac{7}{3}) + πn

tan (x) = 1 : x = \frac{π}{4} + πn

Combine all the solutions

x = arctan (\frac{7}{3}) + πn, x = \frac{π}{4} + πn

Show solutions in decimal form

x = 1.16590 \dots + πn, x = \frac{π}{4} + πn

cos (x) = - \frac{3}{3}

\frac{1}{2} cot (x) = cos (x)

θ, 2 cos (θ) + 1 = 0

- 4 + tan (θ) = \frac{- 12 - 3}{3}

2 cos^{2} (x) - 3 = 0

What is the general solution for 3tan^2(x)-10tan(x)+7=0 ?
The general solution for 3tan^2(x)-10tan(x)+7=0 is x=1.16590…+pin,x= pi/4+pin