Helle, i need help for simplify the expression:

[( cos x) ( sin x) - ( sin x) ( - sin x)] / ( sin x) ²

(cosx*sinx + sinx*sinx)/(sinx*sinx)

(cosx + sinx)/sinx

cotx + 1

(cos sinx²+ sin²x²)/sin²x²

= [(cos sin + sin²)x]/sin²x²
=(cos + sin)/x

sorry, Hector

cos x does not mean cos * x
cosine is a function, so it means cos(x)

Sure, I can help you simplify the expression. Let me break it down step by step.

The given expression is:
[(cos x)(sin x) - (sin x)(-sin x)] / (sin x)²

Step 1: Simplify the numerator.
In the numerator, we have two terms: (cos x)(sin x) and (sin x)(-sin x). Let's simplify each term separately.

(a) (cos x)(sin x)
Using the identity sin(2x) = 2sin(x)cos(x), we can rewrite (cos x)(sin x) as 1/2 * sin(2x).
So, the first term becomes 1/2 * sin(2x).

(b) (sin x)(-sin x)
When we multiply two negative numbers, the result is positive. So, (-sin x)(-sin x) will become sin²(x).

Now, the numerator becomes: 1/2 * sin(2x) - sin²(x).

Step 2: Simplify the denominator.
The denominator is (sin x)². This is equivalent to sin²(x).

So, the simplified expression is:
[(1/2 * sin(2x)) - sin²(x)] / sin²(x).

Note: Sometimes, the expression can be further simplified. However, without additional context or constraints, we cannot simplify this expression any further.