What is the general solution for tan(x/2)+6=0 ?

The general solution for tan(x/2)+6=0 is x=-2*1.40564…+2pin

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tan(x/2)+6=0

tan (\frac{x}{2}) + 6 = 0

x = - 2 \cdot 1.40564 \dots + 2 πn

Degrees

x = - 161.07535 \dots^{\circ} + 36 0^{\circ} n

Solution steps

tan (\frac{x}{2}) + 6 = 0

Move

6

to the right side

tan (\frac{x}{2}) + 6 = 0

Subtract

6

from both sides

tan (\frac{x}{2}) + 6 - 6 = 0 - 6

Simplify

tan (\frac{x}{2}) = - 6

tan (\frac{x}{2}) = - 6

Apply trig inverse properties

tan (\frac{x}{2}) = - 6

General solutions for

tan (\frac{x}{2}) = - 6

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

\frac{x}{2} = arctan (- 6) + πn

\frac{x}{2} = arctan (- 6) + πn

Solve

\frac{x}{2} = arctan (- 6) + πn : x = - 2 arctan (6) + 2 πn

\frac{x}{2} = arctan (- 6) + πn

Simplify

arctan (- 6) + πn : - arctan (6) + πn

arctan (- 6) + πn

Use the following property:

arctan (- x) = - arctan (x)

arctan (- 6) = - arctan (6)

= - arctan (6) + πn

\frac{x}{2} = - arctan (6) + πn

Multiply both sides by

2

\frac{x}{2} = - arctan (6) + πn

Multiply both sides by

2

\frac{2 x}{2} = - 2 arctan (6) + 2 πn

Simplify

x = - 2 arctan (6) + 2 πn

x = - 2 arctan (6) + 2 πn

x = - 2 arctan (6) + 2 πn

Show solutions in decimal form

x = - 2 \cdot 1.40564 \dots + 2 πn

sin^{3} (x) - 2 = - 3 sin^{3} (x)

cos (x) + sin (x) = 2

sin (3 θ) cos (θ) - cos (3 θ) sin (θ) = \frac{3}{2}

tan (x) = 3 cot (x)

2 cos (\frac{1}{2} x) - 1 = 0

What is the general solution for tan(x/2)+6=0 ?
The general solution for tan(x/2)+6=0 is x=-2*1.40564…+2pin