What is the general solution for 3*tan(x)+1=0,x,0<= x<= 2*pi ?

The general solution for 3*tan(x)+1=0,x,0<= x<= 2*pi is No Solution for x\in\mathbb{R}

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3tan(x)+1=0,x,0<= x<= 2pi

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

No Solution for x \in R

Solution steps

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

Move

1

to the right side

3 tan (x) + 1 = 0

Subtract

1

from both sides

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

Simplify

3 tan (x) = - 1

3 tan (x) = - 1

Divide both sides by

3

3 tan (x) = - 1

Divide both sides by

3

\frac{3 tan ( x )}{3} = \frac{- 1}{3}

Simplify

tan (x) = - \frac{1}{3}

tan (x) = - \frac{1}{3}

Apply trig inverse properties

tan (x) = - \frac{1}{3}

General solutions for

tan (x) = - \frac{1}{3}

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

x = arctan (- \frac{1}{3}) + πn

x = arctan (- \frac{1}{3}) + πn

Solutions for the range

x

No Solution for x \in R

cot^{2} (x) - 3 cot (x) - 4 = 0

cot (b) = 0.5008

\frac{1}{6 tan ^{6} ( x )} = \frac{1}{6 sec ^{6} ( x )}

cos^{2} (2 x) - 2 sin^{2} (x) - 1 = 0

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

What is the general solution for 3*tan(x)+1=0,x,0<= x<= 2*pi ?
The general solution for 3*tan(x)+1=0,x,0<= x<= 2*pi is No Solution for x\in\mathbb{R}