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  4. If tan θ- cot θ=7, then the value of tan 3 θ- cot 3 θ is:

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

Trigonometry

Solution:

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