What is the general solution for 4sec(x)+2sqrt(3)=sec(x) ?

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

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4sec(x)+2sqrt(3)=sec(x)

4 sec (x) + 23 = sec (x)

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

Solution steps

4 sec (x) + 23 = sec (x)

Solve by substitution

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

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

sec (x) sin (x) = 2

sec (x) cot (x) = \frac{7}{6}

tan (x) cos (x) = 0

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

2 csc^{2} (x) - 2 csc (x) - 2 = 0

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