Question

If $\tan \theta -\cot \theta =7$ find the value of ${\tan }^3\theta -{\cot }^3\theta$

• A. $284$
• B. $296$
• C. $345$
• D. $364$

Answer 1

The correct option is D $364$

${\tan }^3\theta -{\cot }^3\theta =(\tan \theta -\cot \theta )({\tan }^2\theta +{\cot }^2\theta +\tan \theta \cot \theta )=(\tan \theta -\cot \theta )\left(\right(\tan \theta -\cot \theta {)}^2+2\tan \theta cot\theta +\tan \theta \cot \theta )=7(7^2+3\tan \theta \cot \theta )=7(49+3)=7\times 52=364$

Therefore, Answer is $364$