How do I simplify sin(arccos(sqrt(2)/2)arcsin(2x))?
I get
We have the sine of a difference, so step one will be the difference angle formula,
#= sin arccos(sqrt{2}/2) cos arcsin(2x) + cos arccos(sqrt{2}/2) sin arcsin(2x)
Now,
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To simplify sin(arccos(sqrt(2)/2)  arcsin(2x)), we can use trigonometric identities and properties:

Start by simplifying the inner expressions: arccos(sqrt(2)/2) = π/4 arcsin(2x) = sin^(1)(2x)

Now, we have: sin(π/4  sin^(1)(2x))

Apply the difference of angles formula for sine: sin(a  b) = sin(a)cos(b)  cos(a)sin(b)

Substitute the values: sin(π/4)cos(sin^(1)(2x))  cos(π/4)sin(sin^(1)(2x))

Utilize trigonometric identities to simplify: sin(π/4)cos(sin^(1)(2x))  cos(π/4)sin(sin^(1)(2x)) = (sqrt(2)/2)(√(1  (2x)^2))  (sqrt(2)/2)(2x)

Simplify further: = (sqrt(2)/2)(√(1  4x^2)  2x)
That's the simplified expression for sin(arccos(sqrt(2)/2)  arcsin(2x)).
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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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