What is the general solution for sec(x)=-sqrt(2),0<x<2pi ?

The general solution for sec(x)=-sqrt(2),0<x<2pi is x=(3pi)/4 ,x=(5pi)/4

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sec(x)=-sqrt(2),0<x<2pi

sec (x) = - 2, 0 < x < 2 π

x = \frac{3 π}{4}, x = \frac{5 π}{4}

Solution steps

sec (x) = - 2, 0 < x < 2 π

General solutions for

sec (x) = - 2

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

Solutions for the range

0 < x < 2 π

x = \frac{3 π}{4}, x = \frac{5 π}{4}

1 - cos (2 x) = 0

sin (2 x) cos (x) = cos (x)

- sin (2 x) sin (x) + cos (2 x) cos (x) = cos (x)

cos (x) = \frac{7}{16}

3 = - 2 cos (θ)

What is the general solution for sec(x)=-sqrt(2),0<x<2pi ?
The general solution for sec(x)=-sqrt(2),0<x<2pi is x=(3pi)/4 ,x=(5pi)/4