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Example 6Actually this is a kind of conditional identity, because it has the actual angles. If the angles change, this identity may not be true. In some identities, it doesn't matter what are the angles. You should know that none of the angles in this problem are special angles. They are not like , , , and , so we can't convert their functions to special numbers. If there are conditions for a given identity, we will need to use them when we prove the identity, or it's none sense to have conditions. We will use the conditions--the angles , , etc, to prove this identity. After comparing the two sides we see that the big difference is the difference of operations. To reduce it, we will combine the terms on the left. By comparing what we get with the right side, we believe that , because we already get . If we can prove that, then the problem is solved. So we separate the left to two factors. |
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