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Question Number 114682 by 175mohamed last updated on 20/Sep/20

	Answered by mindispower last updated on 20/Sep/20

	$\forall k \in [2, n]$ $t g (a_{k}) - t g (a_{k - 1}) = \frac{s i n (a_{k})}{c o s (a_{k})} - \frac{s i n (a_{k - 1})}{c o s (a_{k - 1})}$ $= s i n (a_{k} - a_{k - 1}) s e c (a_{k}) s e c (a_{k - 1})$ $= s i n (d) s e c (a_{k}) s e c (a_{k - 1})$ $\Leftrightarrow \frac{t g (a_{k}) - t g (a_{k - 1})}{s i n (d)} = s e c (a_{k}) s e c (a_{k - 1})$ $\underset{k = 2}{\sum^{n}} \frac{t g (a_{k}) - t g (a_{k - 1})}{s i n (d)} = \underset{k = 2}{\sum^{n}} s e c (a_{k}) s e c (a_{k - 1})$ $\Leftrightarrow \frac{t g (a_{n}) - t g (a_{1})}{s i n (d)} = s e c (a_{1}) s e c (a_{2}) +$ $s e c (a_{2}) s e c (a_{3}) + . . . + s e c (a_{n - 1}) s e c (a_{n})$
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