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
To prove the trigonometric identity ((3))/() - ((3))/() = 2, we will start with the left-hand side (LHS) and simplify it to the right-hand side (RHS). Step 1: Write the left-hand side of the identity and substitute the triple angle formulas for (3) and (3). We know that (3) = 3 - 4^3 and (3) = 4^3 - 3. LHS = (3 - 4^3)/() - (4^3 - 3)/() Step 2: Factor out from the numerator of the first term and from the numerator of the second term, then simplify. LHS = ((3 - 4^2))/() - ((4^2 - 3))/() LHS = (3 - 4^2) - (4^2 - 3) Step 3: Expand the expression and group terms. LHS = 3 - 4^2 - 4^2 + 3 LHS = 6 - 4^2 - 4^2 LHS = 6 - 4(^2 + ^2) Step 4: Apply the Pythagorean identity ^2 + ^2 = 1. LHS = 6 - 4(1) LHS = 6 - 4 LHS = 2 Since LHS = RHS, the identity is proven. Hence, ((3))/() - ((3))/() = 2 is proven. Send me the next one 📸