Question

If $\tan \theta +\cot \theta =3$, then ${\tan }^4\theta +{\cot }^4\theta =$

• A. 47
• B. 162
• C. 24
• D. 48

Answer 1

Answer: (A)

47

Given $\tan \theta +\cot \theta =3$
$\Rightarrow (\tan \theta +\cot \theta {)}^2={\tan }^2\theta +{\cot }^2\theta +2=9$
$\Rightarrow {\tan }^2\theta +{\cot }^2\theta =7$
$\Rightarrow {\tan }^4\theta +{\cot }^4\theta +2=49$
$\Rightarrow {\tan }^4\theta +{\cot }^4\theta =47$