Posted by **Sam** on Tuesday, November 12, 2013 at 6:54pm.

Prove that the average of the numbers n sin (n degrees) (n = 2, 4, 6, ... 180) is cot (1 degree)

Hint: Express everything in terms of sin and cos. Can you rearrange the result into a form that allows you to use some of the identities you've learned?

How to start? I know I have to use trigonometric identities but where?

Thanks a lot.

- Trigonometry - Proofs -
**Steve**, Tuesday, November 12, 2013 at 8:10pm
sin0+180sin180 = 0sin0 + 180sin0

2sin2 + 178sin178 = 2sin2 + 178sin2 = 180sin2

...

88sin88 + 102sin102 = 180sin88

so, we have

180(sin0 + sin2 + sin4 + ... + sin88) + 90sin90

= 180(sin0+sin2+...+sin90) - 90

That makes the average

2(sin0+sin2+...+sin90)-1

Gotta think some more. Back later. See what you can figure out.

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