What is the general solution for sec^3(x)=-1 ?

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

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sec^3(x)=-1

sec^{3} (x) = - 1

x = π + 2 πn

Solution steps

sec^{3} (x) = - 1

Solve by substitution

sec (x) = - 1, sec (x) = \frac{1}{2} - i \frac{3}{2}, sec (x) = \frac{1}{2} + i \frac{3}{2}

sec (x) = - 1 : x = π + 2 πn

sec (x) = \frac{1}{2} - i \frac{3}{2} :

No Solution

sec (x) = \frac{1}{2} + i \frac{3}{2} :

No Solution

Combine all the solutions

x = π + 2 πn

\frac{1}{cot ^{2} ( x )} + 3 tan (x) = 0

tan (x) = 0.23

tan (x) = 0.45

2 cos (x) - 1 = sec (x)

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

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