Question

If $\tan \alpha +\cot \alpha =p$, then find ${\tan }^2\alpha +{\cot }^2\alpha$

• A. $p$
• B. $p^2$
• C. $p^2-2$
• D. $2p^2$

Answer 1

Answer: (C)

$p^2-2$

$\tan \alpha +\cot \alpha =p\Rightarrow {\left(\tan \alpha +\cot \alpha \right)}^2=p^2\Rightarrow {\tan }^2\alpha +{\cot }^2\alpha +{2=p}^2\Rightarrow {\tan }^2\alpha +{\cot }^2\alpha =p^2-2$