Question

Aduceți la forma ea mai simpla
E=sin^2 x/1-cos x — cos^2 x/1+sinx

Answer 1

Folosim relatia $sin^{2}x+ cos^{2}x=1$ de aici ⇒$sin^{2}x=1- cos^{2}x$ si de asemeni $cos^{2}x=1- sin^{2}x$. Aceste doua relatii le ilocuim in relatia initiala:
$E= \frac{1- cos^{2}x }{1-cosx}- \frac{1- sin^{2}x }{1+sinx}= \frac{(1-cosx)(1+cosx)}{1-cosx}- \frac{(1-sinx)(1+sinx)}{1+sinx}$ dupa simplificarea celor doua fractii⇒1+cosx-(1-sinx)=1+cosx-1+sinx=cosx+sinx