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

The general solution for tan^2(x)=1+tan(x) is x=1.01722…+pin,x=-0.55357…+pin

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

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

x = 1.01722 \dots + πn, x = - 0.55357 \dots + πn

Solution steps

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

Solve by substitution

tan (x) = \frac{1 + 5}{2}, tan (x) = \frac{1 - 5}{2}

tan (x) = \frac{1 + 5}{2} : x = arctan (\frac{1 + 5}{2}) + πn

tan (x) = \frac{1 - 5}{2} : x = arctan (\frac{1 - 5}{2}) + πn

Combine all the solutions

x = arctan (\frac{1 + 5}{2}) + πn, x = arctan (\frac{1 - 5}{2}) + πn

Show solutions in decimal form

x = 1.01722 \dots + πn, x = - 0.55357 \dots + πn

t, y = 3 sin (2 t - \frac{π}{4})

sec^{4} (x) = 0

sin (0.5 π) cos (0.5 π) = 0.5 sin (2 x + 1)

2 sin^{2} (u) = 1 + sin (u), 0 \leq y (u) < 2 π

sin (α) = cos^{2} (4 5^{\circ})

What is the general solution for tan^2(x)=1+tan(x) ?
The general solution for tan^2(x)=1+tan(x) is x=1.01722…+pin,x=-0.55357…+pin