What is the value of the product sinx*cosx if the difference sinx-cosx is 5/7?

Given that sinx - cosx =
5/7

We need to know that value
sinx*cosx

Let us square both
sides.

==> (sinx - cosx)^2 =
(5/7)^2

==> sin^2 x - 2sinx*cosx + cos^2 x =
25/49

But we know that sin^2cx + cos^2 x =
1

==> -2sinx*cosx  + 1 =
25/49

We will subtract 1 from both
sides.

==> -2sinx*cosx = 25/49 -
1

==> -2sinxcosx =
-24/49

Now we will divide by
-2

==> sinx*cosx = -24/49*-2 =
12/49

Then the value is sinx*cosx =
12/49