Math Is Fun Forum

Avva

Member

Registered: 2009-02-25

Posts: 41

trigonometry

Without using calculator:
prove that:

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: trigonometry

Hi Avva;

I have seen this but can't remember where. This is what I have in my notes.  Maybe it will help.

you get:

Now using:

You get:

Expand:

You get the fourth order poly:

Solve the poly any way you can, to get. (Graph it and deflate out -1/2 and 1, reducing it to a quadratic is perhaps simplest)

I am not sure how to eliminate the 3 other roots, other than the  last root and the first are negative so we can eliminate them. And u = 1 is only true for sin(90°), so we can eliminate u=1. This leaves the third one, hope this is rigorous enough for your needs.

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