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If $\tan A+\cot A=2$, then the value of $\tan ^{4} A+\cot ^{4} A=$
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We have, $\tan A+\cot A=2$
$\begin{aligned}
&(\tan A+\cot A)^{2}=(2)^{2} \\
&\tan ^{2} A+\cot ^{2}+2=4 \\
&\tan ^{2} A+\cot ^{2} A=2 \\
&\left(\tan ^{2} A+\cot ^{2} A\right)^{2}=(2)^{2} \\
&\tan ^{4} A+\cot ^{4} A+2=4 \\
&\tan ^{4} A+\cot ^{4} A=2
\end{aligned}$
$\begin{aligned}
&(\tan A+\cot A)^{2}=(2)^{2} \\
&\tan ^{2} A+\cot ^{2}+2=4 \\
&\tan ^{2} A+\cot ^{2} A=2 \\
&\left(\tan ^{2} A+\cot ^{2} A\right)^{2}=(2)^{2} \\
&\tan ^{4} A+\cot ^{4} A+2=4 \\
&\tan ^{4} A+\cot ^{4} A=2
\end{aligned}$
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