# Limits with trigs

I am having trouble solving limits with trig functions.

limx→0 x+xcosx/sinxcosx

useful equation limθ→0 sinθ/θ = 1

my attempt

x+xcosx/sinxcosx

x/sinxcosx + xcosx/sinxcosx

x/sinx*1/cosx + x/sinx this is where I am getting stuck

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jedishrfu
Mentor
the answer is right in front of you.

As x approaches zero then what is the value of cosx?

and you have the sinx/x as x approaches zero so everything is there for you

the answer is right in front of you.

As x approaches zero then what is the value of cosx?

and you have the sinx/x as x approaches zero so everything is there for you

Does x/sinx = 1 also?

I thought sinx had to be in the numerator for it to = 1

Does x/sinx = 1 also?

I thought sinx had to be in the numerator for it to = 1
Technically, you're right. But note that if ##x\neq 0##, then ##\frac{x}{\sin x}=\frac{1}{\frac{\sin x}{x}}##, and you have something to which you can apply your limit law for ratios.

So I guess technically you're not right (with regard to the value of the limit), but it's good to be skeptical. I had some students a year or so ago that got marked down (per a grading rubric that was not mine) for omitting the step that I showed.