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
We will simplify the left-hand side of the expression ( 6B + 2B)/( 6B + 2B) using sum-to-product trigonometric identities. Step 1: State the sum-to-product identities. The relevant identities are: X + Y = 2 ((X+Y)/(2)) ((X-Y)/(2)) X + Y = 2 ((X+Y)/(2)) ((X-Y)/(2)) Step 2: Apply the identity to the numerator. For the numerator, we have 6B + 2B. Let X = 6B and Y = 2B. 6B + 2B = 2 ((6B+2B)/(2)) ((6B-2B)/(2)) = 2 ((8B)/(2)) ((4B)/(2)) = 2 (4B) (2B) Step 3: Apply the identity to the denominator. For the denominator, we have 6B + 2B. Let X = 6B and Y = 2B. 6B + 2B = 2 ((6B+2B)/(2)) ((6B-2B)/(2)) = 2 ((8B)/(2)) ((4B)/(2)) = 2 (4B) (2B) Step 4: Substitute the simplified numerator and denominator back into the original expression. ( 6B + 2B)/( 6B + 2B) = (2 (4B) (2B))/(2 (4B) (2B)) Cancel out the common terms 2 and (2B) (assuming (2B) ≠ 0). = ((4B))/((4B)) Using the identity ( )/( ) = : = (4B) Step 5: Compare the result with the right-hand side of the given identity. The left-hand side simplifies to (4B). The question asks to show that it equals (4B). Since $