What is the general solution for 3tan^2(x)-8tan(x)+5=0 ?

The general solution for 3tan^2(x)-8tan(x)+5=0 is x=1.03037…+pin,x= pi/4+pin

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3tan^2(x)-8tan(x)+5=0

3 tan^{2} (x) - 8 tan (x) + 5 = 0

x = 1.03037 \dots + πn, x = \frac{π}{4} + πn

Solution steps

3 tan^{2} (x) - 8 tan (x) + 5 = 0

Solve by substitution

tan (x) = \frac{5}{3}, tan (x) = 1

tan (x) = \frac{5}{3} : x = arctan (\frac{5}{3}) + πn

tan (x) = 1 : x = \frac{π}{4} + πn

Combine all the solutions

x = arctan (\frac{5}{3}) + πn, x = \frac{π}{4} + πn

Show solutions in decimal form

x = 1.03037 \dots + πn, x = \frac{π}{4} + πn

sin (2 θ) = - \frac{24}{25}, sin (θ) = \frac{3}{5}

100 + 60 sin (\frac{7 π}{3} x) = 110, 0 \leq x \leq 1

sin (4 x) = \frac{1}{2}

cot^{2} (x) + csc (x) = 1, 0 \leq x < 2 π

81 π = 10.5 - 9 cos (\frac{π}{30} t)

What is the general solution for 3tan^2(x)-8tan(x)+5=0 ?
The general solution for 3tan^2(x)-8tan(x)+5=0 is x=1.03037…+pin,x= pi/4+pin