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

The general solution for tan^2(x)= 1/2 is x=0.61547…+pin,x=-0.61547…+pin

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tan^2(x)= 1/2

tan^{2} (x) = \frac{1}{2}

x = 0.61547 \dots + πn, x = - 0.61547 \dots + πn

Solution steps

tan^{2} (x) = \frac{1}{2}

Solve by substitution

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

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

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

Combine all the solutions

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

Show solutions in decimal form

x = 0.61547 \dots + πn, x = - 0.61547 \dots + πn

3 cos (x) - sin (2 x) = 0

5 cos^{2} (x) + 3 cos (x) = 0

- \frac{2}{3} cos (3 θ) = 1

x, y = sin (x y)

tan (t) = \frac{1}{3}

What is the general solution for tan^2(x)= 1/2 ?
The general solution for tan^2(x)= 1/2 is x=0.61547…+pin,x=-0.61547…+pin