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Example 5--Page 2
This time we don't multiply the left by . Instead, we multiply it by .
Now, we want the first factor to be . To do so, we need change functions to .
Try to simplify the terms on the top of first factor. If we use the Product to Sum formulas to convert them to addition, we'll get , from , ; and , from , , which yields like terms of .
We want the first factor to be . Because the right side of the identity doesn't have a denominator, so we need to cancel . By using the Sum to Product formulas on the top of first factor, we get:
Then we use a Double Angle formula to convert to and canceling . We have:
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