Hi!
Let's first expand the cotangent of theta.
You'll probably know that tangent will be "y/x", or [tex]\frac{sin(x)}{cos(x)}[/tex], and cotangent is the reciprocal of this, meaning that it is "x/y" or [tex]\frac{cos(x)}{sin(x)}[/tex].
That means that we are now given this equation.
[tex]cos(x)\frac{cos(x)}{sin(x)}+sin(x)[/tex]
That'll multiply to:
[tex]\frac{cos^2(x)}{sin(x)}+sin(x)[/tex]
We'll want a common denominator to add by multiplying [tex]sin(x)[/tex] to both top and bottom of the second term:
[tex]\frac{cos^2(x)}{sin(x)}+\frac{sin^2(x)}{sin(x)}[/tex]
[tex]\frac{cos^2(x)+sin^2(x)}{sin(x)}[/tex]
Pythagorean Identity states that [tex]sin^2(x)+cos^2(x)=1[/tex], so substitute that in:
[tex]\frac{1}{sin(x)}[/tex]
Which simplifies to:
[tex]csc(x)[/tex]
Hope this helps!
