sin5-cos0-cos5-sin5-cos5-cos10-sin5-cos55-cos60-

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) + \dots + (\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!