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How do you simplify #cot x xx sin x#?

Answer 1

James Adkins

# (cos x)/(sin x) xx sinx#

=# cosx#

All of the 6 trig ratios can be expressed in terms of #sin theta # and / or #cos theta#

#tan theta = (sin theta)/(cos theta) " "(o/h)/(a/h) = (o xxh)/(axxh) = o/a#

#cot theta = 1/(tan theta) = (cos theta)/(sin theta)#

#sec theta = 1/(cos theta)#

#cosec theta =1/(sin theta)#

#cotx xxsinx #

=# (cos x)/cancel(sin x) xxcancel sinx#

=# cosx#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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