Prove that tan <mrow class="MJX-TeXAtom-ORD"> &#x2212;<!-- − --> 1

KeedadiaHit3vbms

KeedadiaHit3vbms

Answered question

2022-06-02

Prove that tan 1 1 3 + tan 1 1 7 + . . . + tan 1 1 n 2 + n + 1 = tan 1 n n + 2

Answer & Explanation

prisililoraiyk

prisililoraiyk

Beginner2022-06-03Added 3 answers

HINT:
r = 1 n tan 1 1 r 2 + r + 1
= r = 1 n tan 1 ( r + 1 ) r 1 + r ( r + 1 )
= r = 1 n [ tan 1 ( r + 1 ) tan 1 r ]
Kaleigh Beasley

Kaleigh Beasley

Beginner2022-06-04Added 1 answers

Hint: Observe last term of L.H.S. carefully and note that tan 1 a tan 1 b = tan 1 a b 1 + a b

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