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  4. If tan α+ cot α=a then the value of tan 4 α+ cot 4 α is equal to

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Q. If $\tan \alpha+\cot \alpha=a$ then the value of $\tan ^4 \alpha+\cot ^4 \alpha$ is equal to

Trigonometric Functions

Solution:

$\tan \alpha+\cot \alpha=a$
$\Rightarrow \tan ^2 \alpha+\cot ^2 \alpha+2=a^2$
$\Rightarrow \tan ^4 \alpha+\cot ^4 \alpha=\left(a^2-2\right)^2-2=a^4-4 a^2+2$