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

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

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solvefor x,t=tan(x/2)

solve for

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

x = 2 arctan (t) + 2 πn

Solution steps

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

Switch sides

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

Apply trig inverse properties

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

General solutions for

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

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

\frac{x}{2} = arctan (t) + πn

\frac{x}{2} = arctan (t) + πn

Solve

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

\frac{x}{2} = arctan (t) + πn

Multiply both sides by

2

\frac{x}{2} = arctan (t) + πn

Multiply both sides by

2

\frac{2 x}{2} = 2 arctan (t) + 2 πn

Simplify

x = 2 arctan (t) + 2 πn

x = 2 arctan (t) + 2 πn

x = 2 arctan (t) + 2 πn

sin^{2} (x) = 8 cos^{2} (x)

sin (x) + cos (x) = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

sin (θ) = - 0.342

sin (x) = - 0.135

1 - csc^{2} (x) = cot^{2} (x)

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