What is the general solution for -5sec^2(x)-10sec(x)=-15 ?

The general solution for -5sec^2(x)-10sec(x)=-15 is x=1.91063…+2pin,x=-1.91063…+2pin,x=2pin

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-5sec^2(x)-10sec(x)=-15

- 5 sec^{2} (x) - 10 sec (x) = - 15

x = 1.91063 \dots + 2 πn, x = - 1.91063 \dots + 2 πn, x = 2 πn

Solution steps

- 5 sec^{2} (x) - 10 sec (x) = - 15

Solve by substitution

sec (x) = - 3, sec (x) = 1

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

sec (x) = 1 : x = 2 πn

Combine all the solutions

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

Show solutions in decimal form

x = 1.91063 \dots + 2 πn, x = - 1.91063 \dots + 2 πn, x = 2 πn

tan (x + 2 0^{\circ}) = cot (x)

2 sin (θ) = cot (θ)

3 csc^{2} (x) + 1 = 5

6 cos^{2} (x) - 12 cos (x) + 6 = 0

csc (x) = sin (x) tan (x) + cos (x)

What is the general solution for -5sec^2(x)-10sec(x)=-15 ?
The general solution for -5sec^2(x)-10sec(x)=-15 is x=1.91063…+2pin,x=-1.91063…+2pin,x=2pin