## Precalculus (6th Edition) Blitzer

The primary step to solve the equation $4{{\cos }^{2}}x+4\sin x-5=0$ is to replace the trigonometric function of ${{\cos }^{2}}x$ with the $1-{{\sin }^{2}}x$.
So, in order to simplify the trigonometric functions and equations, we change cos into sin, so that all the terms become sin and it is easier to solve. \begin{align} & 4{{\cos }^{2}}x+4\sin x-5=0 \\ & 4\left( 1-{{\sin }^{2}}x \right)+4\sin x-5=0 \end{align} Thus, the primary step to solve the equation $4{{\cos }^{2}}x+4\sin x-5=0$ is to replace the trigonometric function of ${{\cos }^{2}}x$ with $1-{{\sin }^{2}}x$.