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Question

If nm=1tan1(2mm4+m2+2) is equal to

A
tan1(n2+nn2+n+2)
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B
tan1(n2nn2n+2)
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C
tan1(n2+n+2n2+n)
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D
none of these
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Solution

The correct option is A tan1(n2+nn2+n+2)
Consider, tan1(2mm4+m2+2)
=tan1(2m1+(m4+2m2m2+1))
=tan1(2m1+(m2+1)2m2)
=tan1(2m1+(m2+1+m)(m2+1m))
=tan1(m2+1+m)tan1(m2m+1)
Now, nm=1tan1(2mm4+m2+2)=tan1(3)tan1(1)+tan1(7)tan1(3)+......tan1(n2+1+n)tan1(n2n+1)
=tan1(n2+n+1)tan1(1)
=tan1(n2+nn2+n+2)

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