trigonometry

can i use factoring to simplify this trig identity?
the problem is sinx + cotx * cosx i know the answer is cscx and i know how to get it but i want to know if i can do factoring to get it bc i tried to but it wont give me the answer .
this is the step i went through:
1) sinx + cotx * cosx turns into sinx +(cosx/sinx)*cosx
2) i try to factor out sinx so that i would get sinx(1+ cosx * cosx)
3) that left me with sinx(1+cos^(2) x) that's where i im lost can anyone enlighten me plz

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  1. cot = cos/sin, so you have

    sin + cos^2/sin
    = (sin^2+cos^2)/sin
    = 1/sin
    = csc

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  2. im well aware of that steve thank you for answering but i really wanted to know was is it at all possible to use factoring to solve this like i have up there

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  3. I don't see any way to use factoring. You don't in fact come up with

    sin(1+cos^2)

    because you have that pesky 1/sin under the cos^2.

    If you try to fractor out the sin, you get

    sin(1+cos^2/sin^2)

    and again you end up with sin^2+cos^2 on top.

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  4. We could do some " silly" factoring

    sinx + (cosx/sinx)(cosx)
    = sinx + cos^2 x (sinx)^-1
    = (sinx)^-1 (sin^2 x + cos^2 x)
    = (sinx)^-1
    = 1/sinx
    = cscx

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