SOLUTION: Prove that the following equation is an identity 4sin(x/4)cos(x/4)cos(x/2)=sinx

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Question 243254: Prove that the following equation is an identity
4sin(x/4)cos(x/4)cos(x/2)=sinx
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
4sin%28x%2F4%29cos%28x%2F4%29cos%28x%2F2%29=sin%28x%29

Write the 4 in the left side as 2%2A2

2%2A2sin%28x%2F4%29cos%28x%2F4%29cos%28x%2F2%29=sin%28x%29

Put parentheses around 2sin%28x%2F4%29cos%28x%2F4%29

2%2A%282sin%28x%2F4%29cos%28x%2F4%29%29cos%28x%2F2%29=sin%28x%29

Use the identity sin%282alpha%29=2sin%28alpha%29cos%28alpha%29
using alpha=x%2F4, sin%282%2A%28x%2F4%29%29=2sin%28x%2F4%29cos%28x%2F4%29
or sin%28x%2F2%29=2sin%28x%2F4%29cos%28x%2F4%29
to replace what we just put in parentheses:

2%2A%28sin%28x%2F2%29%29cos%28x%2F2%29=sin%28x%29
 
2sin%28x%2F2%29cos%28x%2F2%29=sin%28x%29

Now use that same identity again, sin%282alpha%29=2sin%28alpha%29cos%28alpha%29,
this time using alpha=x%2F2, sin%282%2A%28x%2F2%29%29=2sin%28x%2F2%29cos%28x%2F2%29
or sin%28x%29=2sin%28x%29cos%28x%29 to replace the left side:

sin%28x%29=sin%28x%29

Edwin