How do you verify the identity: #[sin(x) / csc(x) - 1 ] = [ sin (x) + 1 / cot^2 (x) ]#?
Short answer: there is no identity. Here is the logic.
Firstly, it's always advisable to determine the domain of the functions on both sides of the equation.
On the left the restriction is
On the right we need:
Before going any further, it makes sense to check if the identity is true for some simple case. Let's say,
In this case
Therefore, the left side evaluates to
The right side evaluates to
Obviously, these two expressions are not equal to each other for this particular value of