Question

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

Answer 1

X^2-4=2x+4

x^2-2x-4-4=0

x^2-2x-8=0

x1=4

x2=-2

Answer 2

To solve the equation arcsin(x^2) - 4 = arcsin(2x + 4), we can follow these steps:

Step 1: Rewrite the equation using inverse sine function properties. - arcsin(x^2) - arcsin(2x + 4) = 4

Step 2: Apply the sine function to both sides of the equation to eliminate the inverse sine. - sin(arcsin(x^2) - arcsin(2x + 4)) = sin(4)

Step 3: Use the sine of the difference formula. - sin(arcsin(x^2) - arcsin(2x + 4)) = sin(4) - sin(arcsin(x^2)) * cos(arcsin(2x + 4)) - cos(arcsin(x^2)) * sin(arcsin(2x + 4)) = sin(4)

Step 4: Apply the trigonometric identities involving inverse sine and inverse cosine. - x^2 * sqrt(1 - x^2) * (1 / sqrt(1 + (2x + 4)^2)) - sqrt(1 - x^2) * (2x + 4) * (1 / sqrt(1 + (2x + 4)^2)) = sin(4)

Step 5: Simplify the equation by multiplying through by the common denominator. - x^2 * sqrt(1 - x^2) - (2x + 4) * sqrt(1 - x^2) = sin(4) * sqrt(1 + (2x + 4)^2)

Step 6: Combine like terms. - x^2 * sqrt(1 - x^2) - 2x * sqrt(1 - x^2) - 4 * sqrt(1 - x^2) = sin(4) * sqrt(1 + (2x + 4)^2)

Step 7: Move all terms to one side of the equation. - x^2 * sqrt(1 - x^2) - 2x * sqrt(1 - x^2) - 4 * sqrt(1 - x^2) - sin(4) * sqrt(1 + (2x + 4)^2) = 0

Step 8: This is a nonlinear equation that cannot be easily solved analytically. You can use numerical methods or approximation techniques to find an approximate solution for x.

Note: The above steps provide a general approach to solving the equation. However, the resulting equation is quite complex and might not have a simple analytical solution.