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  4. The expression tan2 α+ cot2 α is

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

WBJEEWBJEE 2007

Solution:

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