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

The general solution for 3*tan^2(x)=1 is x=0.52359…+pin,x=-0.52359…+pin

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3*tan^2(x)=1

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

x = 0.52359 \dots + πn, x = - 0.52359 \dots + πn

Degrees

x = 3 0^{\circ} + 18 0^{\circ} n, x = - 3 0^{\circ} + 18 0^{\circ} n

Solution steps

3 tan^{2} (x) = 1

Solve by substitution

3 tan^{2} (x) = 1

Let:

tan (x) = u

3 u^{2} = 1

3 u^{2} = 1 : u = \frac{1}{3}, u = - \frac{1}{3}

3 u^{2} = 1

Divide both sides by

3

3 u^{2} = 1

Divide both sides by

3

\frac{3 u ^{2}}{3} = \frac{1}{3}

Simplify

u^{2} = \frac{1}{3}

u^{2} = \frac{1}{3}

For

x^{2} = f (a)

the solutions are

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

u = \frac{1}{3}, u = - \frac{1}{3}

Substitute back

u = tan (x)

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

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

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

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

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

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

Combine all the solutions

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

Show solutions in decimal form

x = 0.52359 \dots + πn, x = - 0.52359 \dots + πn

2 \cdot 3 sin (v) + 2 cos (v) = 22

2 csc^{3} (x) + 21 csc^{2} (x) + 55 csc (x) + 42 = 0

cos^{2} (\frac{x}{3}) - sin^{2} (\frac{x}{3}) = - \frac{1}{2}

sin (x) = 0.014

6 cos (2 x) + 8 sin (2 x) = 0

What is the general solution for 3*tan^2(x)=1 ?
The general solution for 3*tan^2(x)=1 is x=0.52359…+pin,x=-0.52359…+pin