Question

Aratati ca pentru orice valoare admisibila a numarului real x are loc egalitatea:
sin4x/(1+cos4x) * cos2x/(1+cos2x)=tgx

Answer 1

Salut,

$\dfrac{sin4x}{1+cos4x}\cdot\dfrac{cos2x}{1+cos2x}=\dfrac{2sin2x\cdot cos2x}{1+2cos^22x-1}\cdot\dfrac{cos2x}{1+cos2x}=\\\\=\dfrac{2sin2x\cdot cos2x}{2cos^22x}\cdot\dfrac{cos2x}{1+cos2x}=\dfrac{sin2x}{1+cos2x}=\dfrac{2sinx\cdot cosx}{1+2cos^2x-1}=\\\\=\dfrac{2sinx\cdot cosx}{2cos^2x}=\dfrac{sinx}{cosx}=tgx.$

Green eyes.