How do you simplify #cot4theta# to trigonometric functions of a unit #theta#?
As
Thanks to Abraham de Moivre (16671754),
the real part of the RHS
=the real part in the expansion of LHS
Likewise, the imaginary parts give
The ratio
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To simplify ( \cot(4\theta) ) to trigonometric functions of a unit theta, you can use the following identities:

( \cot(2\theta) = \frac{\cos(2\theta)}{\sin(2\theta)} = \frac{\cos^2(\theta)  \sin^2(\theta)}{2\sin(\theta)\cos(\theta)} )

( \cos(2\theta) = \cos^2(\theta)  \sin^2(\theta) )

( \sin(2\theta) = 2\sin(\theta)\cos(\theta) )
You can then substitute (2\theta) with (4\theta) in these identities and simplify the expressions accordingly.
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When evaluating a onesided 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.
When evaluating a onesided 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.
When evaluating a onesided 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.
When evaluating a onesided 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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