trigonometrie

montrer que: cos(pi/9)sin(4pi/9)-cos(3pi/9)sin(4pi/9)=√3/4

salam

ramener tout le calcul à sin(4pi/9) = X

cospi/9 = -cos8pi/9 = 2.(sin4pi/9)^2 - 1 = 2.X^2 - 1

cos3pi/9 = 1/2

=====>E= cospi/9.sin4pi/9 - cos3pi/9.sin4pi/9 = (4X^3 - 3X)/2

or : sin 3a = 3.sina - 4.(sina)^3

===> E = -sin(12pi/9) /2 = sin(pi/3) /2 = V(3)/4

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