What is the general solution for 6sec^2(x)-8=0 ?

The general solution for 6sec^2(x)-8=0 is x= pi/6+2pin,x=(11pi)/6+2pin,x=(5pi)/6+2pin,x=(7pi)/6+2pin

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6sec^2(x)-8=0

6 sec^{2} (x) - 8 = 0

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

Solution steps

6 sec^{2} (x) - 8 = 0

Solve by substitution

sec (x) = \frac{2 3}{3}, sec (x) = - \frac{2 3}{3}

sec (x) = \frac{2 3}{3} : x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

sec (x) = - \frac{2 3}{3} : x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

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

tan (3 x) = 1, 0 \leq x \leq 2 π

sec^{2} (θ) - 9 sec (θ) + 20 = 0

sin (θ) + sin (θ) cot (θ) = 0

sin (2 x) = - sin (- x)

What is the general solution for 6sec^2(x)-8=0 ?
The general solution for 6sec^2(x)-8=0 is x= pi/6+2pin,x=(11pi)/6+2pin,x=(5pi)/6+2pin,x=(7pi)/6+2pin