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- Thread starter Dainy
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lurflurf

Homework Helper

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what you wrote is not an identity consider x=y=pi/2Dainy said:

sin pi/2+sin pi/2=2

2sin pi/2 cos pi/2=0

do you mean

[tex]\sin(y)+\sin(x)=2\cos(\frac{y-x}{2})\sin(\frac{y+x}{2})[/tex]

if so

start on the left by writing

y=(y+x)/2+(y-x)/2

x=(y+x)/2-(y-x)/2

then expand using

sin(a+b)=sin(a)cos(b)+cos(a)sin(b)

and

sin(a-b)=sin(a)cos(b)-cos(a)sin(b)

add like terms

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- #3

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Dainy:

Make sure that you understand why

cos(a-b) = cos(a) cos(b) + sin(a) sin(b)

and that you can illustrate the meaning of this formula with a drawing.

Many other formulas can be derived form the previous by algebra and by other simple trigonometric rules (likes cos(-b)=cos(b), sin(-b)=-sin(b), cos(pi-b)=-cos(b), ... all rules that can be illustrated by a drawing too.).

So the picture is: a few simple principles and definitions, enough algebra, and you are on your own.

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