Question

Sa se demonstreze ca expresia nu depinde de m.

Answer 1

$E=\dfrac{m+sin2x+m\cdot cos2x}{1+m\cdot sin2x-cos2x}=\dfrac{m+2sinx \cdot cosx+m\cdot 2\cdot cos^2x-m}{1+m\cdot 2\cdot sinx\cdot cosx-1+2sin^2x}=\\\\=\dfrac{2\cdot cosx\cdot(sinx+m\cdot cosx)}{2\cdot sinx\cdot(m\cdot cosx+sinx)}=\dfrac{cosx}{sinx}=ctgx,\;care\;nu\;depinde\;de\;m.$

Green eyes.