Question

Dacă cosx=a,calculati P=sinx/2 sin 5x/2 in funcție de a

Answer 1

Salut,

$P=sin\left(\dfrac{x}2\right)\cdot sin\left(\dfrac{5x}2\right)=sin\left(\dfrac{5x}2\right)\cdot sin\left(\dfrac{x}2\right)=\\\\=\dfrac{1}2\cdot\left[cos\left(\dfrac{5x}2-\dfrac{x}2\right)-cos\left(\dfrac{5x}2+\dfrac{x}2\right)\right]=\dfrac{1}2\cdot[cos(2x)-cos(3x)]=\\\\=\dfrac{1}2\cdot(2cos^2x-1-4cos^3x+3cosx)=\dfrac{2a^2-1-4a^3+3a}2=-2a^3+a^2+\dfrac{3a}2-\dfrac{1}2.$

Green eyes.