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

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

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

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

x = π + 2 πn

Solution steps

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

Solve by substitution

sec (x) = - 1

sec (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = π + 2 πn

2 sin^{2} (x) + 2 sin (x) = 0

8 sin (x) cos (x) = 0

cos (θ) = \frac{9}{41}

3 cos (2 t) + 4 = 1, 0 \leq t \leq π

cos (2 θ) - 5 = - 9 sin (θ)

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