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

The general solution for 2tan(x)=1-tan^2(x) is x=-1.17809…+pin,x=0.39269…+pin

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

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

x = - 1.17809 \dots + πn, x = 0.39269 \dots + πn

Solution steps

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

Solve by substitution

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

tan (x) = - 1 - 2 : x = arctan (- 1 - 2) + πn

tan (x) = 2 - 1 : x = arctan (2 - 1) + πn

Combine all the solutions

x = arctan (- 1 - 2) + πn, x = arctan (2 - 1) + πn

Show solutions in decimal form

x = - 1.17809 \dots + πn, x = 0.39269 \dots + πn

3 sin (θ) + 3 = 2 cos^{2} (θ)

cos (x) = - \frac{5}{6}

2 sin (\frac{x}{2}) - 3 = 0

2 sin^{2} (θ) = sin (θ) + 1

2 sec^{2} (x) - 4 = 0

What is the general solution for 2tan(x)=1-tan^2(x) ?
The general solution for 2tan(x)=1-tan^2(x) is x=-1.17809…+pin,x=0.39269…+pin