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  4. If |tan A + cot A = 2, then the value of tan4 A + cot 4 A =

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Q. If $|tan \,A + \cot \,A = 2$, then the value of $\tan^4 A + \cot^ 4 A = $

KCETKCET 2020

Solution:

$\tan \,A+\cot \,A=2$
$\Rightarrow (\tan \,A+\cot \,A)^{2}=4$
$\Rightarrow \tan ^{2} A+\cot ^{2} A+2 \tan \,A \cot\, A=4$
$\Rightarrow \tan ^{2} A+\cot ^{2} A=2$
$\Rightarrow \left(\tan ^{2} A+\cot ^{2} A\right)^{2}=4$
$\Rightarrow \tan ^{4} A+\cot ^{4} A+2 \tan ^{2} A \cot ^{2} A=4$
$\Rightarrow \tan ^{4} A+\cot ^{4} A=2$