The simplest form of the expression (cot(x) + cos(x))/(1 + cosec(x))

[mustafaymis]

Sinx - Cosx - Tanx - Cotx - Secx

 

[stapel]

What is the simplest form of the following expression?

[imath]\dfrac{\cot(x) + \cos(x)}{1 + \csc(x)}[/imath]

Define "simplest".

(Unfortunately, there is no standard definition of "simplify" and, in this case, it may be that the "simplified" form might not appear to be much simpler than what has been posted -- I haven't checked. It's not like [imath]\cos^2(x) + \sin^2(x)[/imath] that simplifies to just [imath]1[/imath].)

A good first step might be to restate the cotangent and the cosecant in terms of sines and cosines, and see where that leads.

Sinx - Cosx - Tanx - Cotx - Secx

What is the meaning of this subtraction?

 

[mustafaymis]

What is the meaning of this subtraction?

Not is a subtraction, the answer is one of these.

 

[blamocur]

it may be that the "simplified" form might not appear to be much simpler than what has been posted -- I haven't checked.

I checked it, and it can be simplified in a sense acceptable to most of us.

 

[BigBeachBanana]

Factor out [imath]\cos(x)[/imath] in the numerator.