What is the general solution for tan(x/2)=5 ?

The general solution for tan(x/2)=5 is x=2*1.37340…+2pin

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tan(x/2)=5

tan (\frac{x}{2}) = 5

x = 2 \cdot 1.37340 \dots + 2 πn

Solution steps

tan (\frac{x}{2}) = 5

Apply trig inverse properties

\frac{x}{2} = arctan (5) + πn

Solve

\frac{x}{2} = arctan (5) + πn : x = 2 arctan (5) + 2 πn

x = 2 arctan (5) + 2 πn

Show solutions in decimal form

x = 2 \cdot 1.37340 \dots + 2 πn

- 6 cos (2 x) + 23 cos (x) - 11 = 0

sin^{2} (x + 4) = 1

\frac{178.9}{sin ( 12 5 ^{\circ} )} = \frac{125}{sin ( x )}

cos (θ) = \frac{3}{8}

arccos (x) - arcsin (x) = arccos (\frac{3}{2})

What is the general solution for tan(x/2)=5 ?
The general solution for tan(x/2)=5 is x=2*1.37340…+2pin