Question

If $\theta$ is an acute angle and $\tan \theta +\cot \theta =2$ then

• A. $\tan \theta =\frac{1}{2}$
• B. $\tan \theta =2$
• C. ${\tan }^5\theta +{\cot }^5\theta =32$
• D. ${\tan }^7\theta +{\cot }^7\theta =2$

Answer 1

The correct option is D ${\tan }^7\theta +{\cot }^7\theta =2$

$\tan \theta +\cot \theta =2$
Squaring both sides:
$(\tan \theta +\cot \theta {)}^2=2^2$
${\tan }^2\theta +co{t}^2\theta +2\tan \theta \cot \theta =4$
$ta{n}^2\theta +co{t}^2\theta =4-2$
$ta{n}^2\theta +co{t}^2\theta =2$