Mathematics Grade 12, 3CAPS, Investigation: February 2025 INVESTIGATING COMPOUND ANGLES AND THEREFORE, DOUBLE ANGLES. QUESTION 1 1.1. Given: (i) A=60^{circ} and B=30^{circ} (ii) A=110^{circ} and B=50^{circ} (iii) A=225^{circ} and B=135^{circ} Use a calculator to evaluate each of the following: (a) cos (A-B) (b) cos A-cos B (c) cos A.cos B+sin A.sin B 1.2 Compare the values of cos (A-B) with the values of cos A-cos B and cos A.cos B+sin A.sin B 1.3 Using your comparison in Question 1.2., what general conclusion can be made regarding cos (A-B), cos A-cos B and cos A.cos B+sin A.sin B for any values of A and B?

Let’s dive into the fascinating world of compound angles and see how they relate to our calculations! Evaluating \( \cos(A-B) \) demonstrates a key property of angles that helps simplify complex trigonometric expressions. You’ll consistently find that \( \cos(A-B) \) can be broken down using cosine and sine functions, revealing the harmonious relationships between angles in trigonometry. When you compare the results of your calculations, get ready for some "a-ha!" moments. Typically, you’ll uncover that \( \cos(A-B) \) equals \( \cos A \cdot \cos B + \sin A \cdot \sin B \). This relationship stands as a beautiful reminder of how interconnected trigonometric identities really are—highlighting how angles can work together in harmony or create subtle distinctions depending on their measurements. Always double-check your calculations to avoid common pitfall!