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

The general solution for sec^2(x)-4sec(x)=0 is x=1.31811…+2pin,x=2pi-1.31811…+2pin

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sec^2(x)-4sec(x)=0

sec^{2} (x) - 4 sec (x) = 0

x = 1.31811 \dots + 2 πn, x = 2 π - 1.31811 \dots + 2 πn

Solution steps

sec^{2} (x) - 4 sec (x) = 0

Solve by substitution

sec (x) = 4, sec (x) = 0

sec (x) = 4 : x = arcsec (4) + 2 πn, x = 2 π - arcsec (4) + 2 πn

sec (x) = 0 :

No Solution

Combine all the solutions

x = arcsec (4) + 2 πn, x = 2 π - arcsec (4) + 2 πn

Show solutions in decimal form

x = 1.31811 \dots + 2 πn, x = 2 π - 1.31811 \dots + 2 πn

sin (x) = \frac{5}{8}

sin (x) = \frac{5}{7}

sec (t) = 2

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

2 tan^{2} (x) + 5 tan (x) + 3 = 0

What is the general solution for sec^2(x)-4sec(x)=0 ?
The general solution for sec^2(x)-4sec(x)=0 is x=1.31811…+2pin,x=2pi-1.31811…+2pin