What is the general solution for sec^2(x)-8sec(x)=0 ?

The general solution for sec^2(x)-8sec(x)=0 is x=1.44546…+2pin,x=2pi-1.44546…+2pin

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sec^2(x)-8sec(x)=0

sec^{2} (x) - 8 sec (x) = 0

x = 1.44546 \dots + 2 πn, x = 2 π - 1.44546 \dots + 2 πn

Solution steps

sec^{2} (x) - 8 sec (x) = 0

Solve by substitution

sec (x) = 8, sec (x) = 0

sec (x) = 8 : x = arcsec (8) + 2 πn, x = 2 π - arcsec (8) + 2 πn

sec (x) = 0 :

No Solution

Combine all the solutions

x = arcsec (8) + 2 πn, x = 2 π - arcsec (8) + 2 πn

Show solutions in decimal form

x = 1.44546 \dots + 2 πn, x = 2 π - 1.44546 \dots + 2 πn

cot^{2} (x) = 1 + csc (x)

7 tan (A) + 42 = 0

2 sin (x + \frac{π}{4}) = 1

cos (3 x) = \frac{1}{2}

sin (x + \frac{π}{4}) = - \frac{2}{2}, 0 \leq x \leq 2 π

What is the general solution for sec^2(x)-8sec(x)=0 ?
The general solution for sec^2(x)-8sec(x)=0 is x=1.44546…+2pin,x=2pi-1.44546…+2pin