Question

Write the least value of cos² θ + sec² θ.

Answer 1

We know:
cos $\theta$ can take the minimum value of $-1$.

cos² θ + sec² θ

$$\begin{gathered} =\frac{{\cos }^4\theta +1}{{\cos }^2\theta } \\ =\frac{{\left(-1\right)}^4+1}{{\left(-1\right)}^2} \\ =2 \end{gathered}$$