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
here are the solutions to your questions: QUESTION 3 3.1 Without using a calculator, determine the numerical value of 120^. Step 1: Determine the quadrant and reference angle. The angle 120^ lies in the second quadrant. The reference angle _R is 180^ - 120^ = 60^. Step 2: Determine the sign of 120^. In the second quadrant, the sine function is positive. So, 120^ = 60^. Step 3: Recall the exact value of 60^. 60^ = sqrt(3)2 The numerical value of 120^ is sqrt(3)2. 3.2 Prove that: (2 A + 1)/( A + 2A) = A. Step 1: Start with the Left Hand Side (LHS) and apply the double angle identity for 2A. Recall that 2A = 2 A A. LHS = (2 A + 1)/( A + 2 A A) Step 2: Factor out A from the denominator. LHS = (2 A + 1)/( A (1 + 2 A)) Step 3: Cancel the common factor (2 A + 1) from the numerator and denominator. LHS = (1)/( A) Step 4: Express the result in terms of A. Recall that A = (1)/( A). LHS = A Since LHS = RHS, the identity is proven. What's next?