Question

If $\tan \theta +\cot \theta =4$, then the value of ${\tan }^3\theta +{\cot }^3\theta$ is

• A. $52$
• B. $16$
• C. $7\frac{9}{8}$
• D. $27\frac{1}{27}$

Answer 1

Answer: (A)

$52$

$\tan \theta +\cot \theta =4$

$(\tan \theta +\cot \theta {)}^3=4^3$

${\tan }^3\theta +{\cot }^3\theta +(\tan \theta +\cot \theta )3\tan \theta \cot \theta =64$

${\tan }^3\theta +{\cot }^3\theta +\left(4\right)3=64$

${\tan }^3\theta +{\cot }^3\theta =64-12$

${\tan }^3\theta +{\cot }^3\theta =52$