Question

Write the least value of cos² x + sec² x.

 

Answer 1

We know:
cos x can take the minimum value of -1.
cos² x + sec² x
\[= \frac{\cos^4 x + 1}{\cos^2 x}\]
\[ = \frac{\left( - 1 \right)^4 + 1}{\left( - 1 \right)^2}\]
\[ = 2\]