What is the general solution for sec^2(x)+2sec(x)=0 ?

The general solution for sec^2(x)+2sec(x)=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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sec^2(x)+2sec(x)=0

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

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

Solution steps

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

Solve by substitution

sec (x) = 0, sec (x) = - 2

sec (x) = 0 :

No Solution

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

3 tan (\frac{θ + 11 π}{6}) = 3

8 cos^{2} (θ) + 13 = 14 cos (θ) + 8

cos (3 x) = - \frac{1}{2}, 0 \leq x < 2 π

cos (5 t) = 0

tan (4 x) = \frac{3}{3}

What is the general solution for sec^2(x)+2sec(x)=0 ?
The general solution for sec^2(x)+2sec(x)=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin