What is the general solution for -sec^2(x)+1=-5sec(x)-5 ?

The general solution for -sec^2(x)+1=-5sec(x)-5 is x=pi+2pin,x=1.40334…+2pin,x=2pi-1.40334…+2pin

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-sec^2(x)+1=-5sec(x)-5

- sec^{2} (x) + 1 = - 5 sec (x) - 5

x = π + 2 πn, x = 1.40334 \dots + 2 πn, x = 2 π - 1.40334 \dots + 2 πn

Solution steps

- sec^{2} (x) + 1 = - 5 sec (x) - 5

Solve by substitution

sec (x) = - 1, sec (x) = 6

sec (x) = - 1 : x = π + 2 πn

sec (x) = 6 : x = arcsec (6) + 2 πn, x = 2 π - arcsec (6) + 2 πn

Combine all the solutions

x = π + 2 πn, x = arcsec (6) + 2 πn, x = 2 π - arcsec (6) + 2 πn

Show solutions in decimal form

x = π + 2 πn, x = 1.40334 \dots + 2 πn, x = 2 π - 1.40334 \dots + 2 πn

sec (t) = \frac{1}{- \frac{2}{2}}

sin (x) = 0.556692

tan^{2} (x) + 4 tan (x) + 3 = 0

(1 + tan (x))^{2} + (1 - tan (x))^{2} = sec^{2} (x)

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

What is the general solution for -sec^2(x)+1=-5sec(x)-5 ?
The general solution for -sec^2(x)+1=-5sec(x)-5 is x=pi+2pin,x=1.40334…+2pin,x=2pi-1.40334…+2pin