Writing the Trigonometric Expression as an Algebraic Expression

Notice that the pattern displayed has the same form as a standard quadratic expression, $a{x}^2+bx+c.$ Letting $\cos \theta =x,$ we can rewrite the expression as follows:

This expression can be factored as $\left(2x+1\right)\left(x-1\right).$ If it were set equal to zero and we wanted to solve the equation, we would use the zero factor property and solve each factor for $x.$ At this point, we would replace $x$ with $\cos \theta$ and solve for $\theta .$