Question

determinati x apartine de (0,pi), stiind ca sin2x+2 sin^2 x=0

Answer 1

$\it x\in(0,\ \pi) \Rightarrow sinx\ne 0\ \ \ \ \ \ (*)\\ \\ \\ sin2x+2sin^2x=0 \Rightarrow 2sinxcosx+2sin^2x=0 \Rightarrow \\ \\ \Rightarrow 2sinx(cosx+sinx)=0\ \stackrel{(*)}{\Longrightarrow}\ cosx+sinx=0 \Rightarrow \\ \\ \Rightarrow cosx=-sinx\ \stackrel{(*)}{\Longrightarrow}\ x=\dfrac{3\pi}{4}$