^2 + ^2 is - Vidyadip

MCQ

${\tan ^2}\theta + {\cot ^2}\theta $ is

✓
$ \ge 2$
B
$ \le 2$
C
$ \ge - 2$
D
None of these

✓

Answer

Correct option: A.

$ \ge 2$

a
(a) We know that ${\left( {x - \frac{1}{x}} \right)^2} \ge 0 $

$\Rightarrow {x^2} + \frac{1}{{{x^2}}} - 2 \ge 0$

Put $x = \tan \theta \Rightarrow {\tan ^2}\theta + {\cot ^2}\theta \ge 2$.

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