How do you simplify #cos^3x + sin^2xcosx#?
It's not that bad:
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To simplify ( \cos^3 x + \sin^2 x \cos x ), we can use trigonometric identities.
First, recall the Pythagorean identity: ( \sin^2 x + \cos^2 x = 1 ).
We can rewrite ( \cos^3 x ) as ( \cos^2 x \cdot \cos x ).
Now, substitute ( \cos^2 x ) from the Pythagorean identity:
( \cos^3 x + \sin^2 x \cos x = (\cos^2 x \cdot \cos x) + (\sin^2 x \cdot \cos x) )
( = (\cos x \cdot (1 - \sin^2 x)) + (\sin^2 x \cdot \cos x) )
( = \cos x - \cos x \sin^2 x + \sin^2 x \cos x )
Now, use the identity ( \sin^2 x \cos x = \frac{1}{2} \sin(2x) ):
( = \cos x - \frac{1}{2} \sin(2x) + \frac{1}{2} \sin(2x) )
( = \cos x )
So, ( \cos^3 x + \sin^2 x \cos x ) simplifies to ( \cos x ).
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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.
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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