What is the general solution for 4+2tan^2(x)=5tan^2(x)+3 ?

The general solution for 4+2tan^2(x)=5tan^2(x)+3 is x=0.52359…+pin,x=-0.52359…+pin

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4+2tan^2(x)=5tan^2(x)+3

4 + 2 tan^{2} (x) = 5 tan^{2} (x) + 3

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

Solution steps

4 + 2 tan^{2} (x) = 5 tan^{2} (x) + 3

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

3 sin (x) + cos (x) = 4

θ, sec (θ) = 2

2 cos (4 θ) = 0

\frac{1032}{3145} sin (4 x) + \frac{2196}{3145} cos (4 x) = 0

6 - 2 sin (θ) - 8 sin^{2} (θ) = 0

What is the general solution for 4+2tan^2(x)=5tan^2(x)+3 ?
The general solution for 4+2tan^2(x)=5tan^2(x)+3 is x=0.52359…+pin,x=-0.52359…+pin