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Q.
$\left(\tan \frac{3 \pi}{8}\right)^{2013}+\left(-\cot \frac{3 \pi}{8}\right)^{2013}$ is
Binomial Theorem
Solution:
$\left(\tan \frac{3 \pi}{8}\right)^{2013}+\left(-\cot \frac{3 \pi}{8}\right)^{2013}=(\sqrt{2}+1)^{2013}-(\sqrt{2}-1)^{2013}$
$=2\left[{ }^{2013} C _1(\sqrt{2})^{2012}+{ }^{2013} C _3(\sqrt{2})^{2010}+{ }^{2013} C _5(\sqrt{2})^{2008}+\ldots \ldots .+{ }^{2013} C _{2013}(\sqrt{2})^0\right]$
$=$ which is an even integer $ \Rightarrow $ (A)