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=1.21239…+2pin,x=2pi-1.21239…+2pin

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

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

x = 1.21239 \dots + 2 πn, x = 2 π - 1.21239 \dots + 2 πn

Solution steps

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

Solve by substitution

sec (x) = \frac{5 + 41}{4}, sec (x) = \frac{5 - 41}{4}

sec (x) = \frac{5 + 41}{4} : x = arcsec (\frac{5 + 41}{4}) + 2 πn, x = 2 π - arcsec (\frac{5 + 41}{4}) + 2 πn

sec (x) = \frac{5 - 41}{4} :

No Solution

Combine all the solutions

x = arcsec (\frac{5 + 41}{4}) + 2 πn, x = 2 π - arcsec (\frac{5 + 41}{4}) + 2 πn

Show solutions in decimal form

x = 1.21239 \dots + 2 πn, x = 2 π - 1.21239 \dots + 2 πn

2 sin (t) cos (t) = sin (t)

32 = 37.3 \cdot sin (\frac{2 π}{365} (x - 114)) + 26

2 cos^{2} (x) + 3 cos (x) + 1 = 0, (0, 2 π)

- 4 cos (θ) = 4 (1 + cos (θ))

sin (2 a) = 1

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=1.21239…+2pin,x=2pi-1.21239…+2pin