What is the general solution for tan(x/2+pi/3)=-1 ?

The general solution for tan(x/2+pi/3)=-1 is x=2pin+(5pi)/6

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tan(x/2+pi/3)=-1

tan (\frac{x}{2} + \frac{π}{3}) = - 1

x = 2 πn + \frac{5 π}{6}

Solution steps

tan (\frac{x}{2} + \frac{π}{3}) = - 1

General solutions for

tan (\frac{x}{2} + \frac{π}{3}) = - 1

\frac{x}{2} + \frac{π}{3} = \frac{3 π}{4} + πn

Solve

\frac{x}{2} + \frac{π}{3} = \frac{3 π}{4} + πn : x = 2 πn + \frac{5 π}{6}

x = 2 πn + \frac{5 π}{6}

- sec^{2} (x) + 1 = - 5 sec (x) - 5

sec (t) = \frac{1}{- \frac{2}{2}}

sin (x) = 0.556692

tan^{2} (x) + 4 tan (x) + 3 = 0

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

What is the general solution for tan(x/2+pi/3)=-1 ?
The general solution for tan(x/2+pi/3)=-1 is x=2pin+(5pi)/6