Discussion
The minimum value of \(\sec^2\theta + \csc^2\theta\) is:
Answer: C
We rewrite the expression using identities:
\(\sec^2\theta + \csc^2\theta = (1+\tan^2\theta) + (1+\cot^2\theta) = 2 + \tan^2\theta + \cot^2\theta\).
Let \(y = \tan^2\theta\). The expression is \(2 + y + 1/y\). By AM-GM inequality, \(y+1/y \ge 2\sqrt{y \cdot 1/y} = 2\). The minimum value of \(y+1/y\) is 2.
Therefore, the minimum value of the entire expression is 2 + 2 = 4.
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