What is the general solution for 2tan(x)+1=0 ?

The general solution for 2tan(x)+1=0 is x=-0.46364…+pin

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2tan(x)+1=0

2 tan (x) + 1 = 0

x = - 0.46364 \dots + πn

Degrees

x = - 26.56505 \dots^{\circ} + 18 0^{\circ} n

Solution steps

2 tan (x) + 1 = 0

Move

1

to the right side

2 tan (x) + 1 = 0

Subtract

1

from both sides

2 tan (x) + 1 - 1 = 0 - 1

Simplify

2 tan (x) = - 1

2 tan (x) = - 1

Divide both sides by

2

2 tan (x) = - 1

Divide both sides by

2

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

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

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

x = arctan (- \frac{1}{2}) + πn

x = arctan (- \frac{1}{2}) + πn

Show solutions in decimal form

x = - 0.46364 \dots + πn

2 cos (3 x) + cos (2 x) + 1 = 0, 0 \leq x \leq 2 π

tan^{2} (x) = 3

tan (x) csc^{2} (x) - 2 tan (x) = 0

5 sin (2 x) = cos (x)

2 sin (x + \frac{π}{3}) = - 1

What is the general solution for 2tan(x)+1=0 ?
The general solution for 2tan(x)+1=0 is x=-0.46364…+pin