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heureka

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 #1
avatar+26396 
+5

I must have forgotten some rule... trying to figure out how to simplify this... 

x=4(a+b)±16(a+b)248ab24

Simplifies to: x=(a+b)±a2ab+b26

 

x=4(a+b)±16(a+b)248ab24=4(a+b)±16(a+b)2163ab24=4(a+b)±16[ (a+b)23ab ]24|ab=ab=4(a+b)±16(a+b)23ab24|16=4=4(a+b)±4(a+b)23ab24=4[ (a+b)±(a+b)23ab ]24=4[ (a+b)±(a+b)23ab ]46=(a+b)±(a+b)23ab6|(a+b)2=a2+2ab+b2=(a+b)±a2+2ab+b23ab6=(a+b)±a2+2ab3ab+b26|2ab3ab=ab(23)=ab(1)=ab=(a+b)±a2ab+b26

 

laugh

19.08.2016
 #2
avatar+26396 
+5

what will be the value of Sin2(6)-sin2(12)+sin2(18)... till 15th term , angles are in degree.

 

sin2(6)sin2(12)+sin2(18)sin2(24)+sin2(30)sin2(36)+sin2(42)sin2(48)+sin2(54)sin2(60)+sin2(66)sin2(72)+sin2(78)sin2(84)+sin2(90)=sin2(6)sin2(12)+sin2(18)sin2(24)+sin2(30)sin2(36)+sin2(42)sin2(9042)+sin2(9036)sin2(9030)+sin2(9024)sin2(9018)+sin2(9012)sin2(906)+sin2(90)=sin2(6)sin2(12)+sin2(18)sin2(24)+sin2(30)sin2(36)+sin2(42)cos2(42)+cos2(36)cos2(30)+cos2(24)cos2(18)+cos2(12)cos2(6)+sin2(90)=sin2(6)cos2(6)sin2(12)+cos2(12)+sin2(18)cos2(18)sin2(24)+cos2(24)+sin2(30)cos2(30)sin2(36)+cos2(36)+sin2(42)cos2(42)+sin2(90) cos(2φ)=cos2(φ)sin2φcos(2φ)=sin2(φ)cos2φ=cos(12)+cos(24)cos(36)+cos(48)cos(60)+cos(72)cos(84)+sin2(90)|sin2(90)=12=1=1cos(12)+cos(24)cos(36)+cos(48)cos2(60)+cos(72)cos(84)=1cos(12)+cos(24)cos(6024)+cos(6012)cos(60)+cos(60+12)cos(60+24)=1cos(60)cos(12)+cos(24)cos(6024)cos(60+24)+cos(6012)+cos(60+12) cos(α+β)+cos(αβ)=cos(α)cos(β)sin(α)sin(β)+cos(α)cos(β)+sin(α)sin(β)=2cos(α)cos(β)=1cos(60)cos(12)+cos(24)[cos(6024)+cos(60+24)]+[cos(6012)+cos(60+12)]=1cos(60)cos(12)+cos(24)2cos(60)cos(24)+2cos(60)cos(12) cos(60)=12=112cos(12)+cos(24)212cos(24)+212cos(12)=12cos(12)+cos(24)cos(24)+cos(12)=12cos(12)+cos(12)+cos(24)cos(24)=12

 

laugh

17.08.2016