« Trigonométrie/Exercices/Relations trigonométriques 1 » : différence entre les versions

:<math>\cos^4x=\frac38+\frac12frac{\cos2x}2+\frac18frac{\cos4x}8</math>.

<math>\cos^4x=\left(\frac{1+\cos2x}2\right)^2=\frac{1+2\cos2x+\cos^22x}4=\frac{1+2\cos2x+\frac{1+\cos4x}2}4=\frac38+\frac12frac{\cos2x}2+\frac18frac{\cos4x}8</math>.

<math>S\frac S2=\frac32+\frac12\left(\cos^4\frac\pi2pi8+\cos^4\frac{3\pi}48=\frac34+\cos\frac{5\pi}4+\cos\frac{7\pi}4\right)+\frac18\left(\cos\pipi4+\cos\frac{3\pi}4}2+\frac{\cos\frac{5\pi}2pi2+\cos\frac{73\pi}2}8=\right)frac34</math> donc <math>S=\frac32</math>.