What is the general solution for -1=-4sec(x)-sec^2(x)-5 ?

The general solution for -1=-4sec(x)-sec^2(x)-5 is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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-1=-4sec(x)-sec^2(x)-5

- 1 = - 4 sec (x) - sec^{2} (x) - 5

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Solution steps

- 1 = - 4 sec (x) - sec^{2} (x) - 5

Switch sides

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

Solve by substitution

sec (x) = - 2

sec (x) = - 2 : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Combine all the solutions

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

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

3 cos (x) - 1 = 0

tan (θ) = - 11

cos (θ) (2 sin (θ) + 1) = 0

5 cos (2 θ) = 2

What is the general solution for -1=-4sec(x)-sec^2(x)-5 ?
The general solution for -1=-4sec(x)-sec^2(x)-5 is x=(2pi)/3+2pin,x=(4pi)/3+2pin