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

The general solution for tan^2(x)-2tan(x)=1 is x=1.17809…+pin,x=-0.39269…+pin

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

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

x = 1.17809 \dots + πn, x = - 0.39269 \dots + πn

Solution steps

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

Solve by substitution

tan (x) = 1 + 2, tan (x) = 1 - 2

tan (x) = 1 + 2 : x = arctan (1 + 2) + πn

tan (x) = 1 - 2 : x = arctan (1 - 2) + πn

Combine all the solutions

x = arctan (1 + 2) + πn, x = arctan (1 - 2) + πn

Show solutions in decimal form

x = 1.17809 \dots + πn, x = - 0.39269 \dots + πn

sin (a) = 0.25

3 tan^{2} (x + 1 5^{\circ}) - 1 = 0

3 sin^{4} (x) + cos^{4} (x) = 1

sec (3 x) = 5

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

What is the general solution for tan^2(x)-2tan(x)=1 ?
The general solution for tan^2(x)-2tan(x)=1 is x=1.17809…+pin,x=-0.39269…+pin