What is the general solution for sqrt(tan(x))=sqrt(1/3) ?

The general solution for sqrt(tan(x))=sqrt(1/3) is x=0.32175…+pin

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sqrt(tan(x))=sqrt(1/3)

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

x = 0.32175 \dots + πn

Solution steps

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

Square both sides:

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

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

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

Expand

(tan (x))^{2} : tan (x)

(tan (x))^{2}

Apply radical rule:

a = a^{\frac{1}{2}}

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

Apply exponent rule:

(a^{b})^{c} = a^{b c}

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

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2}{2}

Cancel the common factor:

2

= 1

= tan (x)

Expand

(\frac{1}{3})^{2} : \frac{1}{3}

(\frac{1}{3})^{2}

Apply radical rule:

a = a^{\frac{1}{2}}

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

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= (\frac{1}{3})^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2}{2}

Cancel the common factor:

2

= 1

= \frac{1}{3}

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

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

Verify Solutions:

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

True

Check the solutions by plugging them into

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

Remove the ones that don't agree with the equation.

Plug in

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

True

\frac{1}{3} = \frac{1}{3}

\frac{1}{3} = \frac{1}{3}

True

The solution is

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

Show solutions in decimal form

x = 0.32175 \dots + πn

sin (x) sin (2 x) - 2 cos (x) cos (2 x) = 0

a, y = sin (a)

cot^{2} (x) + csc (x) + 1 = 0

csc (θ) = 1.7824

- 22 cos (θ) = 2

What is the general solution for sqrt(tan(x))=sqrt(1/3) ?
The general solution for sqrt(tan(x))=sqrt(1/3) is x=0.32175…+pin