If \( A_{n} \) is the area bounded by the curve \( y=(\tan x)^{n} \) and the lines \( x=0 \) and...

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If \( A_{n} \) is the area bounded by the curve \( y=(\tan x)^{n} \) and the lines \( x=0 \) and \( x=\frac{\pi}{4} \).
Then, prove that for \( n2, A_{n}+A_{n+2}=\frac{1}{n+1} \) and deduce \( \frac{1}{2 n+2}A_{n}\frac{1}{2 n-2} \)
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