What is the general solution for sec^2(x)-7sec(x)=0 ?

The general solution for sec^2(x)-7sec(x)=0 is x=1.42744…+2pin,x=2pi-1.42744…+2pin

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sec^2(x)-7sec(x)=0

sec^{2} (x) - 7 sec (x) = 0

x = 1.42744 \dots + 2 πn, x = 2 π - 1.42744 \dots + 2 πn

Solution steps

sec^{2} (x) - 7 sec (x) = 0

Solve by substitution

sec (x) = 7, sec (x) = 0

sec (x) = 7 : x = arcsec (7) + 2 πn, x = 2 π - arcsec (7) + 2 πn

sec (x) = 0 :

No Solution

Combine all the solutions

x = arcsec (7) + 2 πn, x = 2 π - arcsec (7) + 2 πn

Show solutions in decimal form

x = 1.42744 \dots + 2 πn, x = 2 π - 1.42744 \dots + 2 πn

e^{\frac{π}{2}} - e^{a r c t a n (1 + x^{2})} = 0

3 cot (θ) - 7 = 0

cos (x) = \frac{1249}{1250}

sec (θ) = \frac{9}{7}

4 cos (x - π) = 4

What is the general solution for sec^2(x)-7sec(x)=0 ?
The general solution for sec^2(x)-7sec(x)=0 is x=1.42744…+2pin,x=2pi-1.42744…+2pin