What is the general solution for 5tan^2(x)-1=2tan^2(x) ?

The general solution for 5tan^2(x)-1=2tan^2(x) is x=0.52359…+pin,x=-0.52359…+pin

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5tan^2(x)-1=2tan^2(x)

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

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

Solution steps

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

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

cos^{2} (x) tan^{2} (x) csc^{2} (x) = sin (x)

cos (a) - sin (a) = cot (a) cos (a)

15 cos (\frac{2 π}{365} t) + 43 = 30

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

What is the general solution for 5tan^2(x)-1=2tan^2(x) ?
The general solution for 5tan^2(x)-1=2tan^2(x) is x=0.52359…+pin,x=-0.52359…+pin