If a1,a2,a3,...,an is an arithmetic progression with common differenc

1.	If a1,a2,a3,...,an is an arithmetic progression with common difference d, then evaluate the following expression. tan[tan−1(d1+a1a2)+tan−1(d1+a2a3)+tan−1(d1+a3a4)+⋯+tan−1(d1+an−1an)]
Answer» If $a_{1}, a_{2}, a_{3}, . . ., a_{n}$ is an arithmetic progression with common difference d, then evaluate the following expression. $t a n [t a n^{- 1} (\frac{d}{1 + a_{1} a_{2}}) + t a n^{- 1} (\frac{d}{1 + a_{2} a_{3}}) + t a n^{- 1} (\frac{d}{1 + a_{3} a_{4}}) + \dots + t a n^{- 1} (\frac{d}{1 + a_{n - 1} a_{n}})]$

If a1,a2,a3,...,an is an arithmetic progression with common difference d, then evaluate the following expression. tan[tan−1(d1+a1a2)+tan−1(d1+a2a3)+tan−1(d1+a3a4)+⋯+tan−1(d1+an−1an)]

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If $a_{1}, a_{2}, a_{3}, . . ., a_{n}$ is an arithmetic progression with common difference d, then evaluate the following expression.

$t a n [t a n^{- 1} (\frac{d}{1 + a_{1} a_{2}}) + t a n^{- 1} (\frac{d}{1 + a_{2} a_{3}}) + t a n^{- 1} (\frac{d}{1 + a_{3} a_{4}}) + \dots + t a n^{- 1} (\frac{d}{1 + a_{n - 1} a_{n}})]$

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If a1,a2,a3,...,an is an arithmetic progression with common difference d, then evaluate the following expression. tan[tan−1(d1+a1a2)+tan−1(d1+a2a3)+tan−1(d1+a3a4)+⋯+tan−1(d1+an−1an)]

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