what is the limit of lim x->p/2 (tan(x-(p/2)))/(x-(p/2)-cos(x))

note that x approach p/2 and (x-(p/2)-cos(x)) not (x-(p/2))-cos(x)

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Small correction on my previous answer the derivative of cot is -csc^2, which means that the final answer for my previous solution will be 

1/2

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`lim_(x->Pi/2)(tan(x-Pi/2))/(x-Pi/2-cosx)=0/0 undetermined`

We can use l'hopital rule in this case. First though I would like to rewrite the numerator using one of the trig id as -tan(Pi/2-x)=-cotx.

Thus we get

`lim_(x->Pi/2)(-cotx)/(x-Pi/2-cosx)=`

`lim_(x->Pi/2)(-csc^2x)/(1+sinx)=`

`-1/2`

 

 

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