Solve the equation for x.
arcsin(sq. rt.(2x)) = arccos(sq. rt(x))
To solve the equation arcsin(sq. rt.(2x)) = arccos(sq. rt(x)) for x, we can start by using some trigonometric properties and identities.
1. First, let's square both sides of the equation to eliminate the square root symbols:
(arcsin(sq. rt.(2x)))^2 = (arccos(sq. rt(x)))^2
2. The square of an arc sine (arcsin) and the square of an arc cosine (arccos) give us the original angle value:
(sq. rt.(2x))^2 = (sq. rt(x))^2
2x = x
3. Now, we can solve for x by subtracting x from both sides of the equation:
2x - x = 0
x = 0
Therefore, the solution to the equation arcsin(sq. rt.(2x)) = arccos(sq. rt(x)) is x = 0.