This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Use the Pythagorean identity to find x. We are given x = sqrt((a)/(b)). The Pythagorean identity is ^2 x + ^2 x = 1. Substitute the given value of x: ^2 x + (sqrt((a)/(b)))^2 = 1 ^2 x + (a)/(b) = 1 Subtract (a)/(b) from both sides: ^2 x = 1 - (a)/(b) Combine the terms on the right side: ^2 x = (b)/(b) - (a)/(b) ^2 x = (b-a)/(b) Take the square root of both sides: x = ±sqrt((b-a)/(b)) Step 2: Find x. The cosecant function is the reciprocal of the sine function: x = (1)/( x) Substitute the expression for x: x = (1)/(±sqrt(b-a)b) To simplify, we can flip the fraction inside the square root: x = ±sqrt((b)/(b-a)) The value of x is ±sqrt((b)/(b-a)). That's 2 down. 3 left today — send the next one.