Question

How do you find the limit of `cosx/cotx` as `x->pi/2`?

Answer 1

`lim _(x->pi/2) cos x / cot x = 1`

Explanation:

`lim _(x->pi/2) cos x / cot x`
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`= lim_(x->pi/2) cosx/(cosx/sinx)`
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`= lim_(x->pi/2)cosx/1 xx sinx/cosx`
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`= lim_(x->pi/2)cancel(cosx)/1 xx sinx/cancel(cosx)`
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`=lim_(x->pi/2)sinx`
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`=sin (pi/2)`
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`=1`