What is the general solution for 2sec^2(x)-5sec(x)+2=0 ?

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

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2sec^2(x)-5sec(x)+2=0

2 sec^{2} (x) - 5 sec (x) + 2 = 0

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

Solution steps

2 sec^{2} (x) - 5 sec (x) + 2 = 0

Solve by substitution

sec (x) = 2, sec (x) = \frac{1}{2}

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

sec (x) = \frac{1}{2} :

No Solution

Combine all the solutions

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

sin (\frac{1}{3} x + \frac{3 π}{2}) = 0

2 cos (x) = 3 sin (x)

4 sin^{2} (θ) - 8 cos (θ) + 1 = 0

sin (x) cos (\frac{π}{7}) - sin (\frac{π}{7}) cos (x) = \frac{2}{2}

20 sin (t) cos (t) = - 16 cos (t)

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