Question

Prove sin(x-y)/cosxsiny=tanxcoty-1

Answer 1

See below

Explanation:

Here I attach you the detailed solution.

For this we will need to use the following trigonometric properties and formulas:

sin (x-y) = sin (x) cos (y) - cos (x) sin (y)

tan(x) = sin(x)/cos(x)

cot(x) = 1/tan(x) = [tan(x)] ^(-1) = cos (x)/sin(x)

This properties can be found in any mathematics book and is valid to apply them here, and are the only tools we use to solve the problem. Its worth to note that we have to assume that cos(x)sin(y) is different from 0 in order to use it as a denominator.