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

The general solution for tan(x/2)=4 is x=2*1.32581…+2pin

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tan(x/2)=4

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

x = 2 \cdot 1.32581 \dots + 2 πn

Degrees

x = 151.92751 \dots^{\circ} + 36 0^{\circ} n

Solution steps

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

Apply trig inverse properties

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

General solutions for

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

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

\frac{x}{2} = arctan (4) + πn

\frac{x}{2} = arctan (4) + πn

Solve

\frac{x}{2} = arctan (4) + πn : x = 2 arctan (4) + 2 πn

\frac{x}{2} = arctan (4) + πn

Multiply both sides by

2

\frac{x}{2} = arctan (4) + πn

Multiply both sides by

2

\frac{2 x}{2} = 2 arctan (4) + 2 πn

Simplify

x = 2 arctan (4) + 2 πn

x = 2 arctan (4) + 2 πn

x = 2 arctan (4) + 2 πn

Show solutions in decimal form

x = 2 \cdot 1.32581 \dots + 2 πn

sec (x) sin (x) + sec (x) = 2 sec (x)

3 - sin (x) (4 + 6 sin (x)) = 0

cos (a) = - \frac{3}{5}, sin (a) > 0

cot (x) - cot (33.4 7^{\circ}) = \frac{1485}{2460}

3 + \frac{1}{5} cos (\frac{θ}{3} + \frac{7 π}{4}) = 3

What is the general solution for tan(x/2)=4 ?
The general solution for tan(x/2)=4 is x=2*1.32581…+2pin