((sin5)/(cos0.cos5))+((sin5)/(cos5.cos10))+ . . . +((sin5)/(cos55.cos60)) =?


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Question Number 131230 by Fikret last updated on 02/Feb/21

$\frac{s i n 5}{c o s 0 . c o s 5} + \frac{s i n 5}{c o s 5 . c o s 10} + . . . + \frac{s i n 5}{c o s 55 . c o s 60} = ?$
	Answered by mr W last updated on 02/Feb/21

	$e x a m p l e :$ $\sin 5 = \sin (10 - 5) = \sin 10 \cos 5 - \cos 10 \sin 5$ $\frac{\sin 5}{\cos 5 \cos 10} = \tan 10 - \tan 5$ $\frac{s i n 5}{c o s 0 . c o s 5} + \frac{s i n 5}{c o s 5 . c o s 10} + . . . + \frac{s i n 5}{c o s 55 . c o s 60}$ $= (\tan 5 - \tan 0) + (\tan 10 - \tan 5) + . . . + (\tan 60 - \tan 55)$ $= \tan 60 - \tan 0$ $= \tan 60$ $= \sqrt{3}$
	Commented by malwan last updated on 02/Feb/21

	$g r e a t s i r$ $t h a n k y o u$
	Commented by PRITHWISH SEN 2 last updated on 03/Feb/21

	$Beautiful as always!$
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