What is the general solution for 4tan(x/2)=8 ?

The general solution for 4tan(x/2)=8 is x=2*1.10714…+2pin

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4tan(x/2)=8

4 tan (\frac{x}{2}) = 8

x = 2 \cdot 1.10714 \dots + 2 πn

Degrees

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

Solution steps

4 tan (\frac{x}{2}) = 8

Divide both sides by

4

4 tan (\frac{x}{2}) = 8

Divide both sides by

4

\frac{4 tan ( \frac{x}{2} )}{4} = \frac{8}{4}

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

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

\frac{x}{2} = arctan (2) + πn

\frac{x}{2} = arctan (2) + πn

Solve

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

\frac{x}{2} = arctan (2) + πn

Multiply both sides by

2

\frac{x}{2} = arctan (2) + πn

Multiply both sides by

2

\frac{2 x}{2} = 2 arctan (2) + 2 πn

Simplify

x = 2 arctan (2) + 2 πn

x = 2 arctan (2) + 2 πn

x = 2 arctan (2) + 2 πn

Show solutions in decimal form

x = 2 \cdot 1.10714 \dots + 2 πn

tan (x) = \frac{5}{11}

tan (x) = - 4.8764, π < x < \frac{( 3 π )}{2 , cos ( x )}

x, z = tan (x) y

- 6 sin (θ) + 4 = 33 + 4

- 6 sin (x) + 3 sin (2 x) = 0

What is the general solution for 4tan(x/2)=8 ?
The general solution for 4tan(x/2)=8 is x=2*1.10714…+2pin