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Example 2The difference of angles is sharp. The right side has no , so first we want to cancel in left side. If you read our Memorizing the formulas section, this problem should not be a hard one for you because we included three Triple Angle formulas there. Two of these we will use here. Namely, and . We see we can factor from , and from . Thus we can simplify and . By using the Triple Angle formulas we get: Being very straight forward, we want to factor out and , at the top of the two fractions respectively, and cancel it with the bottom. Then combine the like terms, we have We know can help us to cancel , so we factor out -4, we get, The identity has been proven. It's not hard right? Without knowing our idea you can do it too, but can you give another proof? |
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