Verify the identity:

cos x -cox x/1-tan x = sin x cos x/sin x -cos x

To verify the given identity:

cos x - cox x / 1 - tan x = sin x cos x / sin x - cos x

First, let's simplify the left side of the identity:

cos x - cox x / 1 - tan x

We can rewrite cox x as 1 / tan x (using the reciprocal identity for tangent):

cos x - 1 / tan x / 1 - tan x

To simplify further, we can multiply the numerator and denominator of the fraction by tan x:

(cos x - 1 / tan x) * (tan x / 1 - tan x)

Now, using the distributive property, we can expand the numerator:

= cos x * tan x - 1 * tan x / 1 - tan x

Simplifying the numerator, we get:

= sin x - tan x / 1 - tan x

Now let's simplify the right side of the identity:

sin x cos x / sin x - cos x

We can factor out sin x from the numerator and cos x from the denominator:

(sin x * cos x) / (sin x - cos x)

Now we can simplify the expression:

= sin x / 1 - cos x / 1

= sin x / 1 - cos x

So, the right side of the identity simplifies to sin x / (1 - cos x).

Comparing this with the left side, we can see that they are equal:

(sin x - tan x) / (1 - tan x) = sin x / (1 - cos x)

Thus, the original identity is verified.