Remember: We have to work from either the LHS or the RHS.
(Left hand side or the Right hand side)
You should already know this:
[tex]\huge{Cot(t) = \frac{1}{tan(t)} = \frac{1}{\frac{sin(t)}{cos(t)}} = 1\div \frac{sin(t)}{cos(t)} = 1\times \frac{cos(t)}{sin(t)}=\boxed{\frac{cos(t)}{sin(t)}}[/tex]
You should also know this:
[tex]sin^2(t) + cos^2(t) = 1\\\\\boxed{sin^2(t)} = 1 - cos^2(t)[/tex]
So plugging in both of those into our identity, we get:
[tex]\frac{cos(t)}{sin(t)}\cdot sin^2(t) = cos(t)\cdot sin(t)[/tex]
Simplify the denominator on the LHS (Left Hand Side)
We get:
[tex]cos(t) \cdot sin(t) = cos(t) \cdot sin(t)[/tex]
LHS = RHS
Therefore, identity is verified.
