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

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

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solvefor x=2arctan(z),z

solve for

x = 2 arctan (z), z

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

Solution steps

x = 2 arctan (z)

Switch sides

2 arctan (z) = x

Divide both sides by

2

2 arctan (z) = x

Divide both sides by

2

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

Simplify

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

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

Apply trig inverse properties

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

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

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

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

- 4 - 6 cos (θ) = - 7

cot (x) - csc (x) = 3

- 4 sin (x) = - cos^{2} (x) + 4, 0 \leq x < 2 π

cos (x) = \frac{3}{2}

sin (θ) = - \frac{3}{2}, 0 \leq θ < 2 π

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