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

The general solution for solvefor x,tan^2(x)=tan^2(y) is x=arctan(tan(y))+pin,x=arctan(-tan(y))+pin

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solvefor x,tan^2(x)=tan^2(y)

solve for

x, tan^{2} (x) = tan^{2} (y)

x = arctan (tan (y)) + πn, x = arctan (- tan (y)) + πn

Solution steps

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

Solve by substitution

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

Let:

tan (x) = u

u^{2} = tan^{2} (y)

u^{2} = tan^{2} (y) : u = tan (y), u = - tan (y)

u^{2} = tan^{2} (y)

For

x^{2} = f (a)

the solutions are

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

u = tan^{2} (y), u = - tan^{2} (y)

Simplify

tan^{2} (y) : tan (y)

tan^{2} (y)

Apply radical rule:

assuming

a \geq 0

= tan (y)

Simplify

- tan^{2} (y) : - tan (y)

- tan^{2} (y)

Apply radical rule:

assuming

a \geq 0

= - tan (y)

u = tan (y), u = - tan (y)

Substitute back

u = tan (x)

tan (x) = tan (y), tan (x) = - tan (y)

tan (x) = tan (y), tan (x) = - tan (y)

tan (x) = tan (y) : x = arctan (tan (y)) + πn

tan (x) = tan (y)

Apply trig inverse properties

tan (x) = tan (y)

General solutions for

tan (x) = tan (y)

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

x = arctan (tan (y)) + πn

x = arctan (tan (y)) + πn

tan (x) = - tan (y) : x = arctan (- tan (y)) + πn

tan (x) = - tan (y)

Apply trig inverse properties

tan (x) = - tan (y)

General solutions for

tan (x) = - tan (y)

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

x = arctan (- tan (y)) + πn

x = arctan (- tan (y)) + πn

Combine all the solutions

x = arctan (tan (y)) + πn, x = arctan (- tan (y)) + πn

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

- 6 sin (x) - 5 cos (x) = 2

2 sin^{2} (x) + cos^{2} (x) = 2

2 sin^{2} (x) + sin^{2} (x) + cos^{2} (x) = 1

sin^{2} (x) + 3 cos (x) - 1 = 0

What is the general solution for solvefor x,tan^2(x)=tan^2(y) ?
The general solution for solvefor x,tan^2(x)=tan^2(y) is x=arctan(tan(y))+pin,x=arctan(-tan(y))+pin