What is the general solution for 3tan(x^2)-1=0 ?

The general solution for 3tan(x^2)-1=0 is x=sqrt(0.32175…+pin),x=-sqrt(0.32175…+pin)

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3tan(x^2)-1=0

3 tan (x^{2}) - 1 = 0

x = 0.32175 \dots + πn, x = - 0.32175 \dots + πn

Degrees

x = 0^{\circ} + 106.62778 \dots^{\circ} n, x = 0^{\circ} - 106.62778 \dots^{\circ} n

Solution steps

3 tan (x^{2}) - 1 = 0

Move

1

to the right side

3 tan (x^{2}) - 1 = 0

Add

1

to both sides

3 tan (x^{2}) - 1 + 1 = 0 + 1

Simplify

3 tan (x^{2}) = 1

3 tan (x^{2}) = 1

Divide both sides by

3

3 tan (x^{2}) = 1

Divide both sides by

3

\frac{3 tan ( x ^{2} )}{3} = \frac{1}{3}

Simplify

tan (x^{2}) = \frac{1}{3}

tan (x^{2}) = \frac{1}{3}

Apply trig inverse properties

tan (x^{2}) = \frac{1}{3}

General solutions for

tan (x^{2}) = \frac{1}{3}

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

x^{2} = arctan (\frac{1}{3}) + πn

x^{2} = arctan (\frac{1}{3}) + πn

Solve

x^{2} = arctan (\frac{1}{3}) + πn : x = arctan (\frac{1}{3}) + πn, x = - arctan (\frac{1}{3}) + πn

x^{2} = arctan (\frac{1}{3}) + πn

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

x = arctan (\frac{1}{3}) + πn, x = - arctan (\frac{1}{3}) + πn

x = arctan (\frac{1}{3}) + πn, x = - arctan (\frac{1}{3}) + πn

Show solutions in decimal form

x = 0.32175 \dots + πn, x = - 0.32175 \dots + πn

What is the general solution for 3tan(x^2)-1=0 ?
The general solution for 3tan(x^2)-1=0 is x=sqrt(0.32175…+pin),x=-sqrt(0.32175…+pin)