Sin(A+B) sin(A-B) /sin^A Cos^B=1-cot^A Tan^B

In order to prove

Let's write both sides in terms of only.

Let's start with the left hand side: we can use the formula for sum and subtraction of the sine to write

and

So, their multiplication is

So, the left hand side simplifies to

Now, on with the right hand side. We have

Now simply make this expression one fraction:

And as you can see, the two sides are equal.

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step-by-step explanation: