What is the general solution for tan^2(x)+1=4tan(x) ?

The general solution for tan^2(x)+1=4tan(x) is x=1.30899…+pin,x=0.26179…+pin

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tan^2(x)+1=4tan(x)

tan^{2} (x) + 1 = 4 tan (x)

x = 1.30899 \dots + πn, x = 0.26179 \dots + πn

Solution steps

tan^{2} (x) + 1 = 4 tan (x)

Solve by substitution

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

tan (x) = 2 + 3 : x = arctan (2 + 3) + πn

tan (x) = 2 - 3 : x = arctan (2 - 3) + πn

Combine all the solutions

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

Show solutions in decimal form

x = 1.30899 \dots + πn, x = 0.26179 \dots + πn

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

2 sin^{4} (x) = 4 - 7 cos^{2} (x)

4 cos^{2} (A) - 1 = 0

sin (\frac{75 π}{11}) = sin (\frac{x π}{11})

sec^{2} (θ) = \frac{4}{3}

What is the general solution for tan^2(x)+1=4tan(x) ?
The general solution for tan^2(x)+1=4tan(x) is x=1.30899…+pin,x=0.26179…+pin