How to prove coax=sinxcotx

Answer 1

To prove that coax = sin x cot x, we need to manipulate the left-hand side (LHS) and right-hand side (RHS) of the equation until they are identical.

Starting with the LHS:

LHS = coax

Using the definition of the cotangent function, we know that cot x is equal to cos x divided by sin x:

LHS = cos x / sin x

Now, let's manipulate the RHS:

RHS = sin x cot x

Using the definition of the cotangent function again, we can substitute cot x with cos x / sin x:

RHS = sin x (cos x / sin x)

The sin x in the numerator and denominator cancels out:

RHS = cos x

Now we can see that the LHS (cos x / sin x) is equal to the RHS (cos x).

Therefore, we have proven that coax = sin x cot x.