Question

In Problems 91-93, find the real zeros of each trigonometric function on the interval$0\le \theta <2\pi$

Short answer

The real zeroes are$x=\frac{\pi }{2},\frac{3\pi }{2}$

Step-by-step solution

Given information

Given function$f\left(x\right)=\cos \left(2x\right)+{\sin }^{2}x$

Using trigonometric identity and calculate

Using, we get

$$\begin{gathered} \cos 2x+{\sin }^{2}x=0 \\ 1-2{\sin }^{2}x+{\sin }^{2}x=0 \\ 1-{\sin }^{2}x=0 \\ \pm 1=\sin x \\ x=\frac{\pi }{2},x=\frac{3\pi }{2} \end{gathered}$$