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If $\tan \theta+\cot \theta=4$, then $\tan ^{4} \theta+\cot ^{4} \theta=$
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Verified Answer
The correct answer is:
194
$\tan \theta+\cot \theta=4$
On squaring both side, we get
$\tan ^{2} \theta+\cot ^{2} \theta+2 \tan \theta \cot \theta=16 \Rightarrow \tan ^{2} \theta+\cot ^{2} \theta=14$
On squaring both side, we get
$\begin{array}{l}
\tan ^{4} \theta+\cot ^{4} \theta+2 \tan ^{2} \theta \cot ^{2} \theta=196 \\
\tan ^{4} \theta+\cot ^{4} \theta=196-2=194
\end{array}$
On squaring both side, we get
$\tan ^{2} \theta+\cot ^{2} \theta+2 \tan \theta \cot \theta=16 \Rightarrow \tan ^{2} \theta+\cot ^{2} \theta=14$
On squaring both side, we get
$\begin{array}{l}
\tan ^{4} \theta+\cot ^{4} \theta+2 \tan ^{2} \theta \cot ^{2} \theta=196 \\
\tan ^{4} \theta+\cot ^{4} \theta=196-2=194
\end{array}$
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