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Example 3--Page 4What we will do is multiply by 4 at the top and bottom, so it will cancel those ’s. Next we want to combine these two terms to get one term (product) and angle . If we change to and combine the first and second terms, we have: Please note that the Product-to-Sum formulas , and , and all help us to get angle . Now we have: The identity has been proven. From the second proof, we can see that we used a lot of proof strategies. They are all based on our idea--reduce the 3 differences. Our idea is simple but powerful. |
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