Çözüldü Trigonometrik Özdeşlikler (Celal Aydın ÇKS)

https://s19.postimg.org/sat422jnn/trigonometri.png

{ [ sin(3π / 8) - sin(π / 8) ]·[ sin(3π / 8) + sin(π / 8) ] } / { (-1 / 2)·[ cos(π / 12 + 5π / 12) - cos(π / 12 - 5π / 12) ] } =

(-2)·{ 2sin[ (3π / 8 - π / 8) / 2 ]·cos[ (3π / 8 + π / 8) / 2 ]·2sin[ (3π / 8 + π / 8) / 2 ]·cos[ (3π / 8 - π / 8) / 2 ] } / [ cos(π / 2) - cos(π / 3) ] =

-2·{ [ 2sin(π / 8)·cos(π / 4) ]·[ 2sin(π / 4)·cos(π / 8) ] } / (0 - 1 / 2) =

4·{ [ 2sin(π / 8)·cos(π / 8) ]·[ 2sin(π / 4)·cos(π / 4) ] } =

4·[ sin(π / 4) ]·sin(π / 2) =

4[ (√2) / 2 ] ·1 =

2√2

WolframAlpha Kontrolu: http://www.wolframalpha.com/input/?i=((sin(3pi/8))^2 - (sin(pi/8))^2) / ((sin(pi/12))*sin(5pi/12))