`cosθ/ (1-tanθ)` + `sinθ/ (1−cotθ)` is equals to ​

Explanation

`cosx+cosy - cos(x+y) = 3/2`

`=>2cos((x+y)/2)cos((x-y)/2) - (2cos^2(x+y)-1) = 3/2`

`=>2cos^2(x+y) - 2cos((x+y)/2)cos((x-y)/2) +3/2-1 = 0`

`=>2cos^2(x+y) - 2cos((x+y)/2)cos((x-y)/2) +1/2 = 0`

Now, this ia quadratic equation in `cos(x+y)/2`.

So, to have real roots, its discriminant should be greater than or equal to `0`.

`:. (-2cos((x-y)/2))^2 -4(2)(1/2) ge 0`

`=>4cos^2((x-y)/2) - 4 ge 0`

...