What is the general solution for sec^2(x)-3sec(x)=0 ?

The general solution for sec^2(x)-3sec(x)=0 is x=1.23095…+2pin,x=2pi-1.23095…+2pin

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sec^2(x)-3sec(x)=0

sec^{2} (x) - 3 sec (x) = 0

x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn

Solution steps

sec^{2} (x) - 3 sec (x) = 0

Solve by substitution

sec (x) = 3, sec (x) = 0

sec (x) = 3 : x = arcsec (3) + 2 πn, x = 2 π - arcsec (3) + 2 πn

sec (x) = 0 :

No Solution

Combine all the solutions

x = arcsec (3) + 2 πn, x = 2 π - arcsec (3) + 2 πn

Show solutions in decimal form

x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn

3 cot (x) + 1 = 0

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

tan (θ) = \frac{5}{3}

tan (x) = \frac{3}{5}

6 sec^{2} (θ) tan (θ) = 12 tan (θ)

What is the general solution for sec^2(x)-3sec(x)=0 ?
The general solution for sec^2(x)-3sec(x)=0 is x=1.23095…+2pin,x=2pi-1.23095…+2pin