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Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
General ideas

   Final thoughts
      Page 1 | Page 2 | Page 3 | Proof(s)

Example 5--Page 2

This time we don't multiply the left by 6_5102.gif (2186 bytes). Instead, we multiply it by 6_5201.gif (1397 bytes).

6_5202.gif (4443 bytes)

Now, we want the first factor to be 6_5203.gif (1797 bytes). To do so, we need change functions tan_4tht.gif (1221 bytes) to 6_5204.gif (1327 bytes).

6_5205.gif (6986 bytes)

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 2theta.gif (991 bytes), 6theta.gif (1023 bytes) from 2theta.gif (991 bytes), 4theta.gif (1008 bytes); and 6theta.gif (1023 bytes), 14theta.gif (1037 bytes) from 4theta.gif (1008 bytes), 10theta.gif (1057 bytes), which yields like terms of cos_6tht.gif (1212 bytes).

6_5206.gif (10324 bytes)

We want the first factor to be 6_5203.gif (1797 bytes). Because the right side of the identity doesn't have a denominator, so we need to cancel 6_5206a.gif (465 bytes). By using the Sum to Product formulas on the top of first factor, we get:

6_5207.gif (3991 bytes)

Then we use a Double Angle formula to convert 6_5208.gif (1232 bytes) to 6_5209.gif (1735 bytes) and canceling sin_4tht.gif (1197 bytes). We have:

6_5210.gif (2306 bytes)


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