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

The general solution for (3tan^2(x)-1)=0 is x=0.52359…+pin,x=-0.52359…+pin

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

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

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

Solution steps

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

Solve by substitution

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} : 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

8 sin (\frac{x}{2}) - 8 = 0

cos (2 x) + 2 = 3 cos (x)

cos (x) = - cos (2 x)

cos (2 x) + 2 cos (x) = 0

- 1 + cos (x) = 0

What is the general solution for (3tan^2(x)-1)=0 ?
The general solution for (3tan^2(x)-1)=0 is x=0.52359…+pin,x=-0.52359…+pin