# How do you express #sin^4theta+cot^2theta # in terms of non-exponential trigonometric functions?

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[ \sin^4(\theta) + \cot^2(\theta) ]

[ = (\sin^2(\theta))^2 + (\frac{\cos^2(\theta)}{\sin^2(\theta)})^2 ]

[ = (\sin^2(\theta))^2 + (\frac{\cos^2(\theta)}{\sin^2(\theta)})^2 ]

[ = (\sin^2(\theta))^2 + \frac{\cos^4(\theta)}{\sin^4(\theta)} ]

[ = (\sin^2(\theta))^2 + \frac{(1 - \sin^2(\theta))^2}{\sin^4(\theta)} ]

[ = \sin^4(\theta) + 2\sin^2(\theta)\cos^2(\theta) + \frac{1 - 2\sin^2(\theta) + \sin^4(\theta)}{\sin^4(\theta)} ]

[ = \sin^4(\theta) + 2\sin^2(\theta)\cos^2(\theta) + \frac{1}{\sin^4(\theta)} - \frac{2}{\sin^2(\theta)} + 1 ]

[ = \sin^4(\theta) + 2\sin^2(\theta)\cos^2(\theta) + \csc^2(\theta) - 2\csc^2(\theta) + 1 ]

[ = \sin^4(\theta) + 2\sin^2(\theta)\cos^2(\theta) - \csc^2(\theta) + 1 ]

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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.

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.

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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