What is the general solution for (1+tan(x/2))/(1-tan(x/2))=sqrt(4.137131) ?

The general solution for (1+tan(x/2))/(1-tan(x/2))=sqrt(4.137131) is x=2*0.32845…+2pin

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(1+tan(x/2))/(1-tan(x/2))=sqrt(4.137131)

\frac{1 + tan ( \frac{x}{2} )}{1 - tan ( \frac{x}{2} )} = 4.137131

x = 2 \cdot 0.32845 \dots + 2 πn

Solution steps

\frac{1 + tan ( \frac{x}{2} )}{1 - tan ( \frac{x}{2} )} = 4.137131

Solve by substitution

tan (\frac{x}{2}) = \frac{5.137131 - 2 4.137131}{3.137131}

tan (\frac{x}{2}) = \frac{5.137131 - 2 4.137131}{3.137131} : x = 2 arctan (\frac{5.137131 - 2 4.137131}{3.137131}) + 2 πn

Combine all the solutions

x = 2 arctan (\frac{5.137131 - 2 4.137131}{3.137131}) + 2 πn

Show solutions in decimal form

x = 2 \cdot 0.32845 \dots + 2 πn

cos (θ) = 0.51

csc (θ) = \frac{- 2 3}{3}

cos (x) = \frac{32}{50}

tan (\frac{A}{2}) = 1.02

(sin (a) + cos (a))^{2} + (sin (a) + cos (a))^{2} = 2

What is the general solution for (1+tan(x/2))/(1-tan(x/2))=sqrt(4.137131) ?
The general solution for (1+tan(x/2))/(1-tan(x/2))=sqrt(4.137131) is x=2*0.32845…+2pin