Explicație pas cu pas:
Scriem cotangenta ca fiind:
[tex]ctgx=2 => \frac{cosx}{sinx}=2=>cosx=2sinx[/tex]
Inlocuim cosinus in expresie:
[tex]E(x)=\frac{2sinx+3sinx}{(2sinx)^3-sin^3x}=\frac{5sinx}{7sin^3x}=\frac{5}{7sin^2x}=\frac{5}{7}*\frac{1}{sin^2x}[/tex]
Cautam sa descoperim valoarea pentru [tex] \frac{1}{sin^2x} [/tex] si folosim si formula [tex] sin^2x+cos^2x=1 [/tex].
[tex]ctgx=2\\ctg^2x=4\\\frac{cos^2x}{sin^2x}=4\\\frac{1-sin^2x}{sin^2x}=4\\\frac{1}{sin^2x}-\frac{sin^2x}{sin^2x}=4\\\frac{1}{sin^2x}-1=4\\\frac{1}{sin^2x}=5[/tex]
Finalizam:
[tex]E(x)=\frac{5}{7}*\frac{1}{sin^2x}=\frac{5}{7}*5=\frac{25}{7}[/tex]
