The equation "Arcsin x + arcsin 2x = pi/2" is a trigonometric equation that involves the inverse sine function. It states that the sum of the inverse sine of x and the inverse sine of 2x is equal to pi/2 radians or 90 degrees.
The domain of this equation is all real numbers between -1 and 1, inclusive. This is because the inverse sine function only exists for values between -1 and 1. The range is also between -1 and 1, inclusive, as the sum of two inverse sine functions can never exceed 1 or be less than -1.
There are infinitely many solutions to this equation. Some possible solutions include x = 0 and x = 1/2. Other solutions can be found by using trigonometric identities to manipulate the equation and solve for x.
This equation can be solved by using algebraic manipulation and trigonometric identities. One method is to use the double angle formula for sine to rewrite the equation in terms of sine only, and then solve for x using the inverse sine function. Another method is to use the Pythagorean identity to convert the equation to a quadratic equation and solve for x.
This equation is significant because it involves the inverse sine function, which has many real-world applications in fields such as physics, engineering, and statistics. It is also a useful tool for solving trigonometric equations and can help to understand the relationships between different trigonometric functions.