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

The general solution for tan^2(x)=2 is x=0.95531…+pin,x=-0.95531…+pin

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tan^2(x)=2

tan^{2} (x) = 2

x = 0.95531 \dots + πn, x = - 0.95531 \dots + πn

Solution steps

tan^{2} (x) = 2

Solve by substitution

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

tan (x) = 2 : x = arctan (2) + πn

tan (x) = - 2 : x = arctan (- 2) + πn

Combine all the solutions

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

Show solutions in decimal form

x = 0.95531 \dots + πn, x = - 0.95531 \dots + πn

0 = 2 cos (2 x)

4 cos^{4} (x) - 5 cos^{2} (x) + 1 = 0

3 sin (x) + 2 = sin (x)

sin (x) cos (x) - sin (x) = 0

tan^{2} (x) = 2 tan (x) sin (x)

What is the general solution for tan^2(x)=2 ?
The general solution for tan^2(x)=2 is x=0.95531…+pin,x=-0.95531…+pin