Arcsin(x^2)-4=arcsin(2x+4)

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вопрос

To solve the given equation, we can start by writing it in terms of sine functions:

arcsin(x^2) - 4 = arcsin(2x + 4)

Using the definition of arcsin, we have:

sin(arcsin(x^2)) = x^2
sin(arcsin(2x + 4)) = 2x + 4

Now we have:

x^2 = sin(arcsin(x^2))
2x + 4 = sin(arcsin(2x + 4))

From the first equation, we have:

x^2 = x^2

This is always true, so it does not provide any additional information. Now, let's solve the second equation:

2x + 4 = sin(arcsin(2x + 4))

Since the sine and arcsine functions are inverse functions of each other, sin(arcsin(u)) = u for all u in the domain of arcsin function. Thus, we have:

2x + 4 = 2x + 4

This equation is also always true, so the original equation arcsin(x^2) - 4 = arcsin(2x + 4) holds for all x in its domain.