What is the general solution for solvefor x,z=tan(x/2) ?

The general solution for solvefor x,z=tan(x/2) is x=2arctan(z)+2pin

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solvefor x,z=tan(x/2)

solve for

x, z = tan (\frac{x}{2})

x = 2 arctan (z) + 2 πn

Solution steps

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

Switch sides

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

Apply trig inverse properties

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

General solutions for

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

tan (x) = a \Rightarrow x = arctan (a) + πn

\frac{x}{2} = arctan (z) + πn

\frac{x}{2} = arctan (z) + πn

Solve

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

\frac{x}{2} = arctan (z) + πn

Multiply both sides by

2

\frac{x}{2} = arctan (z) + πn

Multiply both sides by

2

\frac{2 x}{2} = 2 arctan (z) + 2 πn

Simplify

x = 2 arctan (z) + 2 πn

x = 2 arctan (z) + 2 πn

x = 2 arctan (z) + 2 πn

tan (\frac{x}{2}) = 3, 0 \leq x \leq 2 π

0 = 4 sin (2 θ)

tan (θ) + 3 = 0

cos (2 x) - 4 cos (x) + 3 = 0

6 cos^{2} (A) - 5 cos (A) + 1 = 0

What is the general solution for solvefor x,z=tan(x/2) ?
The general solution for solvefor x,z=tan(x/2) is x=2arctan(z)+2pin