Question

Solve the equation for all real values of x.
sec2x + 2secx = 0

Answer 1

Given :

$sec^2\ x + 2sec\ x = 0$

To Find :

All real value solution of given equation.

Solution :

Simplifying given equation, we get :

sec x( sec x + 2 ) = 0

sec x = 0  and (sec x + 2) = 0

For, sec x = 0 :

x = not defined.

For, (sec x + 2) = 0 :

cos x = -1/2

x = cos⁻¹( -1/2 ) = 2π/3

Therefore, general solution is ( 2nπ ± 2π/3 ), n ∈ Z⁺ .