Question

If $\theta$ is an acute angle and $\tan \theta +\cot \theta =2$, then ${\tan }^7\theta +{\cot }^7\theta =2$.

• A. True
• B. False

Answer 1

The correct option is A True

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

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

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

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

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

$\tan \theta =1$

$\theta ={45}^0$

Therefore,

${\tan }^7\theta +{\cot }^7\theta ={\tan }^7{45}^o+{\cot }^7{45}^o=1+1=2$