What is the general solution for 4tan^2(x)-1=tan^2(x) ?

The general solution for 4tan^2(x)-1=tan^2(x) is x=0.52359…+pin,x=-0.52359…+pin

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4tan^2(x)-1=tan^2(x)

4 tan^{2} (x) - 1 = tan^{2} (x)

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

Solution steps

4 tan^{2} (x) - 1 = tan^{2} (x)

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

tan (θ) sin (θ) + sin (θ) = 0

tan (x) = 0.5

3 sin (x) = cos (x)

sec^{2} (x) - 3 sec (x) = 0

3 cot (x) + 1 = 0

What is the general solution for 4tan^2(x)-1=tan^2(x) ?
The general solution for 4tan^2(x)-1=tan^2(x) is x=0.52359…+pin,x=-0.52359…+pin