Question

What if this function simplified?

Answer 1

Hi!

Let's first expand the cotangent of theta.

You'll probably know that tangent will be "y/x", or $\frac{sin(x)}{cos(x)}$, and cotangent is the reciprocal of this, meaning that it is "x/y" or $\frac{cos(x)}{sin(x)}$.

That means that we are now given this equation.

$cos(x)\frac{cos(x)}{sin(x)}+sin(x)$

That'll multiply to:

$\frac{cos^2(x)}{sin(x)}+sin(x)$

We'll want a common denominator to add by multiplying $sin(x)$ to both top and bottom of the second term:

$\frac{cos^2(x)}{sin(x)}+\frac{sin^2(x)}{sin(x)}$

$\frac{cos^2(x)+sin^2(x)}{sin(x)}$

Pythagorean Identity states that $sin^2(x)+cos^2(x)=1$, so substitute that in:

$\frac{1}{sin(x)}$

Which simplifies to:

$csc(x)$

Hope this helps!