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

The general solution for 1-2tan^2(x)=-tan^2(x) is x= pi/4+pin,x=(3pi)/4+pin

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1-2tan^2(x)=-tan^2(x)

1 - 2 tan^{2} (x) = - tan^{2} (x)

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

Solution steps

1 - 2 tan^{2} (x) = - tan^{2} (x)

Solve by substitution

tan (x) = 1, tan (x) = - 1

tan (x) = 1 : x = \frac{π}{4} + πn

tan (x) = - 1 : x = \frac{3 π}{4} + πn

Combine all the solutions

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

sin (x) = - \frac{1}{2}, 0 \leq x \leq 2 π

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

sin^{2} (a) sec (a) = tan^{2} (a)

tan^{2} (θ) - sec (θ) = 1

sin (x) = \frac{8}{10}

What is the general solution for 1-2tan^2(x)=-tan^2(x) ?
The general solution for 1-2tan^2(x)=-tan^2(x) is x= pi/4+pin,x=(3pi)/4+pin