What is the general solution for 4tan^2(x)-16tan(x)+7=0 ?

The general solution for 4tan^2(x)-16tan(x)+7=0 is x=1.29249…+pin,x=0.46364…+pin

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4tan^2(x)-16tan(x)+7=0

4 tan^{2} (x) - 16 tan (x) + 7 = 0

x = 1.29249 \dots + πn, x = 0.46364 \dots + πn

Solution steps

4 tan^{2} (x) - 16 tan (x) + 7 = 0

Solve by substitution

tan (x) = \frac{7}{2}, tan (x) = \frac{1}{2}

tan (x) = \frac{7}{2} : x = arctan (\frac{7}{2}) + πn

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

Combine all the solutions

x = arctan (\frac{7}{2}) + πn, x = arctan (\frac{1}{2}) + πn

Show solutions in decimal form

x = 1.29249 \dots + πn, x = 0.46364 \dots + πn

1 - cos (x) = 0.5

arctan (100 x) - arctan (x) = 4 5^{\circ}

tan^{2} (x) - 9 = 0

2 = - 4 - 3 csc (θ)

x, 3 tan (2 x) = - 1

What is the general solution for 4tan^2(x)-16tan(x)+7=0 ?
The general solution for 4tan^2(x)-16tan(x)+7=0 is x=1.29249…+pin,x=0.46364…+pin