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5. Summarizing--Page 2
The answer of the third question is no in general cases. In the discussion of Understanding the formulas section we know many formulas can help us transform sum to product. For examples, in Double Angle formulas,
the process from left to right is transforming sum to product.
In the sum angles formula:
The process from right to left is transforming sum to product. By using this process we can transform into a product as follows.
In general, we can transform to be product:
where satisfies the system:
or the equation .
From the examples above, we can see that our abilities in solving problems will be enhanced if we can summarize all formulas by the transformations of angles, functions, and operations.
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