Question

If tan alpha+ cot alpha=2,then tan^20alpha+cot^20alpha=

Answer 1

Answer:

The answer is 2

Step-by-step explanation:

Given  $\tan\alpha+\cot\alpha=2$

          $\Rightarrow \tan\alpha+\dfrac{1}{\tan\alpha}=2$

Since  $\tan\alpha\cot\alpha=1$

           $\Rightarrow \dfrac{\tan^2\alpha+1}{2}=\tan\alpha\\\\\Rightarrow \tan^2\alpha+1=2\tan\alpha\\\Rightarrow \tan^2\alpha-2\tan\alpha+1=0\\\Rightarrow (\tan\alpha-1)^2=0\\\Rightarrow \tan\alpha=1\therefore \cot\alpha=\dfrac{1}{\tan\alpha}=1$

Therefore $\tan^{20}\alpha+\cot^{20}\alpha=(1)^{20}+1^{20}=1+1=2$