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

The general solution for tan^2(x/2)=1 is x= pi/2+2pin,x=(3pi)/2+2pin

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tan^2(x/2)=1

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

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

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

Solve by substitution

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

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

tan (\frac{x}{2}) = - 1 : x = \frac{3 π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

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

1 - sin (x - \frac{3 π}{2}) = - sin (x - \frac{π}{2})

sin (x + \frac{π}{2}) = \frac{3}{2}

3 tan (2 x) = - 1

2 tan^{2} (3 x) = 6

What is the general solution for tan^2(x/2)=1 ?
The general solution for tan^2(x/2)=1 is x= pi/2+2pin,x=(3pi)/2+2pin