Question

If $\tan \theta -\cot \theta =7$, then the value of ${\tan }^3\theta -{\cot }^3\theta$ is:

• A. 250
• B. 354
• C. 343
• D. 364

Answer 1

Answer: (D)

Given, $\tan \theta -\cot \theta =7$
We know that,
$a^3-b^3=(a-b{)}^3+3ab(a-b)$
${\tan }^3\theta -{\cot }^3\theta =(\tan \theta -\cot \theta {)}^3+3\tan \theta \cot \theta$
$(\tan \theta -\cot \theta )$
$=7^3+3(7)=343+21=364$