Respuesta :
Answer:
[tex]sin(x)=\frac{1}{2}[/tex]
Step-by-step explanation:
we are given
[tex]\frac{1+cos(x)}{sin(x)}+\frac{sin(x)}{1+cos(x)} =4[/tex]
We will make common denominator
[tex]\frac{(1+cos(x))\times (1+cos(x))}{(sin(x))\times (1+cos(x))}+\frac{sin(x)\times sin(x)}{(1+cos(x))\times sin(x)} =4[/tex]
now, we can simplify it
[tex]\frac{1+cos^2(x)+2cos(x)+sin^2(x)}{(sin(x))\times (1+cos(x))}=4[/tex]
[tex]\frac{2+2cos(x)}{(sin(x))\times (1+cos(x))}=4[/tex]
[tex]\frac{2(1+cos(x))}{(sin(x))\times (1+cos(x))}=4[/tex]
now, we can cancel it
[tex]\frac{2}{sin(x)}=4[/tex]
[tex]\frac{2}{4}=sin(x)[/tex]
we can simplify it
and we get
[tex]sin(x)=\frac{1}{2}[/tex]
