Question

The expression ${\tan }^2\alpha +{\cot }^2\alpha$ is

• A. $\ge 2$
• B. $\le 2$
• C. $\ge -2$
• D. None of these

Answer 1

Answer: (A)

Since, $(\tan \alpha -\cot \alpha {)}^2\ge 0$
$\Rightarrow {\tan }^2\alpha +{\cot }^2\alpha -2\tan \alpha \cot \alpha \ge 0$
$\Rightarrow {\tan }^2\alpha +{\cot }^2\alpha -2\ge 0$
$\Rightarrow {\tan }^2\alpha +{\cot }^2\alpha \ge 2$