21.3 Hence, compure number 2.1 .1 and 2.1 .2 and write a conclusion about \( \cos (\alpha-\beta) \). (5) \( \qquad \) 21.4 Use2.1.3 \( \cos (\alpha-\beta)=\cos \alpha \cdot \cos \beta+\sin \alpha \cdot \sin \beta] \) to derive a formula for \( \cos (\alpha+\beta \) (Hint: use suitable reduction formula ) \( \qquad \) \( \qquad \) \( \qquad \) (4) 21.5 Use \( \cos (\alpha-\beta) \) to derive a formula for \( \sin (\alpha-\beta) \). (Hint: use co-function) \( \qquad \) \( \qquad \) \( \qquad \) (3 2.1.6 Use \( \cos (\alpha-\beta) \) to derive a formula for \( \sin (\alpha+\beta) \). (Hint: use co-function) \( \qquad \) \( \qquad \) \( \qquad \) Ginde 12 Machematics SBA 2025 \( \sqrt{2} \)
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Extra Insights
Did you know that the cosine angle addition and subtraction formulas have roots in ancient Greece? Mathematicians such as Euclid and Ptolemy were essential in developing trigonometric concepts. They used geometry to explore how angles interact, paving the way for the formulas you are studying today. So, every time you apply \( \cos (\alpha \pm \beta) \), you're tapping into a rich history of mathematical discovery! When it comes to real-world applications, these cosine formulas are invaluable in fields like physics, engineering, and computer graphics! For instance, they help model wave patterns, define rotations, and create stunning 3D animations. So, next time you find yourself calculating angles, remember that you're not just crunching numbers—you're harnessing the same principles that professionals rely on across various industries!
