For > 3 , the value of f( ) = ^2 + ^2 always lies in the interval - Vidyadip

MCQ

For $\theta > \frac{\pi }{3}$, the value of $f(\theta ) = {\sec ^2}\theta + {\cos ^2}\theta $ always lies in the interval

A
$(0, 2)$
B
$[0, 1]$
C
$(1, 2)$
✓
$[2,\;\infty )$

✓

Answer

Correct option: D.

$[2,\;\infty )$

d
(d) $ - 1 \le \cos \theta \le 1$ ==> $ = - \frac{1}{{{a^2}}}$

and ${\sec ^2}\theta \ge 1$ for $\theta > \frac{\pi }{3}$ , $\sec \theta \ge 2$

==> ${\sec ^2}\theta \ge 4$. Required interval $ = [2,\,\,\infty )$.

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