The trigonometric functions cosine and secant are related by the next formula:

Substituting this relation into the equation, we get:

Multiplying by cos(x) at both sides of the equation:

Substituting with y = cos(x), we get:

Using the quadratic formula with the coefficients a = 2, b = -1, and c = -1, the solution to this equation is:
![\begin{gathered} y_(1,2)=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y_(1,2)=\frac{1\pm\sqrt[]{(-1)^2-4\cdot2\cdot(-1)}}{2\cdot2} \\ y_(1,2)=\frac{1\pm\sqrt[]{9}}{4} \\ y_1=(1+3)/(4)=1 \\ y_2=(1-3)/(4)=-(1)/(2) \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/7o2mu3h9kzzeugaf7rkswr3astilpja2xl.png)
In terms of the x-variable, the solutions are:

x must be in the interval [0, 2π). Taking this interval into account, the solution to the first equation is:

And the solutions to the second equation are:
