Show that:Cos x-cos^3 x/sin x=sin x cos x.?

To prove this identity, we will start with the left side of the equation and manipulate it to show that it is equal to the right side.

Given: (cos x - cos^3 x) / sin x

First, we will factor out a cos x from the numerator:

= cos x (1 - cos^2 x) / sin x

Next, we will use the Pythagorean identity sin^2 x + cos^2 x = 1 to replace 1 - cos^2 x with sin^2 x:

= cos x sin^2 x / sin x

Now, we can simplify by canceling out sin x in the numerator and denominator:

= cos x sin x

Finally, we can rewrite cos x sin x as sin x cos x, which is the right side of the equation:

= sin x cos x

Therefore, we have shown that (cos x - cos^3 x) / sin x = sin x cos x.

$$=cos x-cos^3 x/sin x$$
$$=cos x(1-cos^2 x)/sin x$$
$$=(cos xsin^2 x)/sin x$$
$$=sin x cos x$$