What is the general solution for 3sec^2(x)-4=0 ?

The general solution for 3sec^2(x)-4=0 is x= pi/6+2pin,x=(11pi)/6+2pin,x=(5pi)/6+2pin,x=(7pi)/6+2pin

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3sec^2(x)-4=0

3 sec^{2} (x) - 4 = 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

3 sec^{2} (x) - 4 = 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

cos^{2} (4 5^{\circ})

arccos (cos (\frac{4 π}{3}))

2 cos^{2} (x) - cos (x) - 1 = 0

arcsin (- \frac{1}{2})

csc (- \frac{5 π}{6})

What is the general solution for 3sec^2(x)-4=0 ?
The general solution for 3sec^2(x)-4=0 is x= pi/6+2pin,x=(11pi)/6+2pin,x=(5pi)/6+2pin,x=(7pi)/6+2pin