# How do you find A, B and C, given that #A sin ( B x + C ) = cos ( cos^(-1) sin x + sin^(-1) cos x ) + sin (cos^(-1) sin x + sin^(-1) cos x )#?

So, the given equation is

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To find the values of ( A ), ( B ), and ( C ) in the equation ( A \sin(Bx + C) = \cos(\cos^{-1}(\sin x) + \sin^{-1}(\cos x)) + \sin(\cos^{-1}(\sin x) + \sin^{-1}(\cos x)) ), we can compare the corresponding parts of both sides of the equation.

From the given equation, we can see that:

- The amplitude ( A ) corresponds to the coefficient of ( \sin(Bx + C) ).
- The phase shift ( C ) corresponds to the constant added inside the trigonometric functions.
- The frequency ( B ) corresponds to the coefficient of ( x ) inside the sine function.

By comparing the equations, we can determine the values of ( A ), ( B ), and ( C ). However, the equation provided seems quite convoluted and may not lead to a straightforward solution. It appears to involve multiple inverse trigonometric functions and trigonometric identities, which could complicate the process of solving for ( A ), ( B ), and ( C ).

If the question is intended to test knowledge of trigonometric identities and manipulation techniques, it would involve simplifying the given equation using trigonometric identities and then comparing coefficients to determine the values of ( A ), ( B ), and ( C ).

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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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