What is the general solution for tan^2(x/2)-tan(x/2)-2=0 ?

The general solution for tan^2(x/2)-tan(x/2)-2=0 is x=2*1.10714…+2pin,x=(3pi)/2+2pin

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tan^2(x/2)-tan(x/2)-2=0

tan^{2} (\frac{x}{2}) - tan (\frac{x}{2}) - 2 = 0

x = 2 \cdot 1.10714 \dots + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

tan^{2} (\frac{x}{2}) - tan (\frac{x}{2}) - 2 = 0

Solve by substitution

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

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

tan (\frac{x}{2}) = - 1 : x = \frac{3 π}{2} + 2 πn

Combine all the solutions

x = 2 arctan (2) + 2 πn, x = \frac{3 π}{2} + 2 πn

Show solutions in decimal form

x = 2 \cdot 1.10714 \dots + 2 πn, x = \frac{3 π}{2} + 2 πn

tan (x) = \frac{- 3}{4}

sin (x) = - 2 sin^{2} (x)

3 cos (θ) = sin (θ)

csc (θ) = \frac{4}{3}

9^{s i n (x) - 1} + 3 = 3^{s i n (x)} + 3^{s i n (x) - 1}

What is the general solution for tan^2(x/2)-tan(x/2)-2=0 ?
The general solution for tan^2(x/2)-tan(x/2)-2=0 is x=2*1.10714…+2pin,x=(3pi)/2+2pin