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

Degrees

x = 54.73561 \dots^{\circ} + 18 0^{\circ} n, x = - 54.73561 \dots^{\circ} + 18 0^{\circ} n

Solution steps

tan^{2} (x) = 2

Solve by substitution

tan^{2} (x) = 2

Let:

tan (x) = u

u^{2} = 2

u^{2} = 2 : u = 2, u = - 2

u^{2} = 2

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

u = 2, u = - 2

Substitute back

u = tan (x)

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

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

tan (x) = 2 : x = arctan (2) + πn

tan (x) = 2

Apply trig inverse properties

tan (x) = 2

General solutions for

tan (x) = 2

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (2) + πn

x = arctan (2) + πn

tan (x) = - 2 : x = arctan (- 2) + πn

tan (x) = - 2

Apply trig inverse properties

tan (x) = - 2

General solutions for

tan (x) = - 2

tan (x) = - a \Rightarrow x = arctan (- a) + πn

x = arctan (- 2) + πn

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