1. sin(x)/tan(x) = cos(x)?

Been working a little problem here for a while, the whole thing looks like this:

Simplify:

sin(x)/tan(x) + cos(x)tan(x)

I know the right side can be simplified to sin(x), but im not sure about the left. I put it into terms of cosine and sine, making it: sin(x)/sin(x)/cos(x)

My thought process here was to then multiply by the reciprocal, which would end with the sin(x)'s cancelling out and leaving just cos(x).

Can anyone verify this?

2. Originally Posted by Lewong
Been working a little problem here for a while, the whole thing looks like this:

Simplify:

sin(x)/tan(x) + cos(x)tan(x)

I know the right side can be simplified to sin(x), but im not sure about the left. I put it into terms of cosine and sine, making it: sin(x)/sin(x)/cos(x)

My thought process here was to then multiply by the reciprocal, which would end with the sin(x)'s cancelling out and leaving just cos(x).

Can anyone verify this?
yes,sinx/tanx=cosx

3. Simplify: sin(x)/tan(x) + cos(x)tan(x), then

sin(x)/tan(x) + cos(x)tan(x) = (sin x)/(sin x / cos x) + cos x ( sin x / cos x)

= (sin x)(cos x / sin x) + cos x ( sin x / cos x)

= cos x + sin x

4. Thanks so much guys! I was pretty sure I had this right, but I just couldn't find anywhere that verified it.

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sinx.tanx

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