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

The general solution for sec^2(x)+2=3sec(x) is x= pi/3+2pin,x=(5pi)/3+2pin,x=2pin

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sec^2(x)+2=3sec(x)

sec^{2} (x) + 2 = 3 sec (x)

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = 2 πn

Solution steps

sec^{2} (x) + 2 = 3 sec (x)

Solve by substitution

sec (x) = 2, sec (x) = 1

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

sec (x) = 1 : x = 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = 2 πn

cos (x) - 1 = - cos (x)

2 cos^{2} (x) = 3

9 tan (2 x) - 9 cot (x) = 0

sin (2 x) = 2 sin^{2} (x)

sin (x) sec (x) = sin (x)

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