Simplify::::

sin (teta) cot (teta) = cos (teta)

sin ØcotØ = cosØ

are you solving?
sinØcosØ/sinØ = cosØ
cosØ = cosØ

yup, that it is

The question probably says, "prove the identity ...."

in that case
LS = sinØcosØ/sinØ
= cosØ
= RS

Ø

sin Ø cot Ø = cos Ø

I'm not solving this equation divided by sin Ø. But thanks a lot for your help and your right you have to prove the identity.

To simplify the equation sin(teta) cot(teta) = cos(teta), we can use the trigonometric identities to rewrite the expression on the left-hand side in terms of sine and cosine functions only.

Let's start by rewriting the cotangent function. The cotangent of an angle is the reciprocal of the tangent, which can be written as:

cot(teta) = 1 / tan(teta)

Next, we can express the tangent function in terms of sine and cosine:

tan(teta) = sin(teta) / cos(teta)

Substituting this expression back into the equation, we get:

sin(teta) cot(teta) = sin(teta) / cos(teta) * 1 / (sin(teta) / cos(teta))

Now, we can cancel out the common terms in the numerator and denominator, as well as the fractions:

sin(teta) cot(teta) = (sin(teta) * cos(teta)) / (sin(teta) * cos(teta))

The sine and cosine terms in the numerator and denominator cancel out, giving us:

sin(teta) cot(teta) = 1

So, the simplified form of sin(teta) cot(teta) = cos(teta) is 1.