Question

If $\tan \theta +\cot \theta =2$ find the value of ${\tan }^{1025}\theta +{\cot }^{1025}\theta$

• A. $0$
• B. $1$
• C. $2$
• D. $\frac{1}{2}$

Answer 1

The correct option is C $2$

Given $\tan \theta +\cot \theta =2$

$\Rightarrow \tan \theta +\frac{1}{\tan \theta }=2$

$\Rightarrow {\tan }^2\theta +1=2\tan \theta$

$\Rightarrow {\tan }^2\theta -2\tan \theta +1=0$

$\Rightarrow (\tan \theta -1{)}^2=0$

$\Rightarrow \tan \theta =1\therefore \cot \theta =\frac{1}{\tan \theta }=\frac{1}{1}=1$

$\therefore {\tan }^{1025}\theta +{\cot }^{1025}\theta =1^{1025}+1^{1025}=1+1=2$