What is the general solution for tan(θ/2)=2 ?

The general solution for tan(θ/2)=2 is θ=2*1.10714…+2pin

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tan(θ/2)=2

tan (\frac{θ}{2}) = 2

θ = 2 \cdot 1.10714 \dots + 2 πn

Degrees

θ = 126.86989 \dots^{\circ} + 36 0^{\circ} n

Solution steps

tan (\frac{θ}{2}) = 2

Apply trig inverse properties

tan (\frac{θ}{2}) = 2

General solutions for

tan (\frac{θ}{2}) = 2

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

\frac{θ}{2} = arctan (2) + πn

\frac{θ}{2} = arctan (2) + πn

Solve

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

\frac{θ}{2} = arctan (2) + πn

Multiply both sides by

2

\frac{θ}{2} = arctan (2) + πn

Multiply both sides by

2

\frac{2 θ}{2} = 2 arctan (2) + 2 πn

Simplify

θ = 2 arctan (2) + 2 πn

θ = 2 arctan (2) + 2 πn

θ = 2 arctan (2) + 2 πn

Show solutions in decimal form

θ = 2 \cdot 1.10714 \dots + 2 πn

sin (x) = 6

tan (y) = 1

cot (x) tan (x) = (sec (x)) (csc (x))

sin (2 x) = 5 cos^{2} (x)

2 sin^{2} (x) - 3 sin (x) + 1 = 0, 0^{\circ} \leq x \leq 18 0^{\circ}

What is the general solution for tan(θ/2)=2 ?
The general solution for tan(θ/2)=2 is θ=2*1.10714…+2pin