Hell of a trick

Geometry Level pending

Let A be average of the numbers 2sin2,4sin4,6sin6,......180sin180 , then A is (all angles are in degree)

sin1 cos1 cot1 tan1

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Tanishq Varshney
Dec 26, 2014

multiply by sin1

Avi Solanki
Oct 28, 2015

we have cos (n-1) - cos (n+1) = 2 sin n sin 1 ,,,1

now 180 sin 180 = 180 sin 0 178 sin 178 = 180 sin 2

so total sum = 180 ( sin 0 + sin 2 + sin 4 + ... + sin 88) + 90 sin 90 = 90 ( 2 sin 0 + 2 sin 2 + 2 sin 4 + 2 sin 88) + 90 sin 90

as there are 90 numbers average = 2 sin 2 + 2 sin 4 + 2 sin 88 + sin 90 as = ( cos 1 - cos 3)/ sin 1 + (cos 3 - cos 5)/ sin 1 + ( cos 87- cos 89 / sin 1 + 1 = ( cos 1 - cos 89)/ sin 1 + 1 = cot 1 - sin 1/sin 1 + 1 as cos 89 = sin 1 = cot 1 - 1 + 1 = cot 1

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...