What is the general solution for tan^2(x)-5tan(x)+6=0 ?

The general solution for tan^2(x)-5tan(x)+6=0 is x=1.24904…+pin,x=1.10714…+pin

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tan^2(x)-5tan(x)+6=0

tan^{2} (x) - 5 tan (x) + 6 = 0

x = 1.24904 \dots + πn, x = 1.10714 \dots + πn

Solution steps

tan^{2} (x) - 5 tan (x) + 6 = 0

Solve by substitution

tan (x) = 3, tan (x) = 2

tan (x) = 3 : x = arctan (3) + πn

tan (x) = 2 : x = arctan (2) + πn

Combine all the solutions

x = arctan (3) + πn, x = arctan (2) + πn

Show solutions in decimal form

x = 1.24904 \dots + πn, x = 1.10714 \dots + πn

3 tan (\frac{x}{4}) - 3 = 0

sin^{2} (3 x) = 1

2 - - 1 - 6 sin (x) = - 4 sin (x)

2 sin (\frac{x}{2}) - 1 = 0

cos^{2} (x) - sin^{2} (x) + sin (x) = 0

What is the general solution for tan^2(x)-5tan(x)+6=0 ?
The general solution for tan^2(x)-5tan(x)+6=0 is x=1.24904…+pin,x=1.10714…+pin