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Question

If S=90r=1tan1(2r2+r2+r4), then 8190cotS is equal to

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Solution

tan1(2r2+r2+r4)=tan1((r2+1+r)(r2+1r)(r2+1+r)(r2+1r)+1)=tan1(r2+1+r)tan1(r2+1r)
S=90r=1[tan1(r2+1+r)tan1(r2+1r)]=tan1(8191)tan1(1)=tan1(81908192)
8190cotS=8192

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