SOLUTION: I would like an explanation to this problem. **use a half angle formula to find cos 22.5 degrees Thanks for your help.

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Question 333685: I would like an explanation to this problem.
**use a half angle formula to find cos 22.5 degrees
Thanks for your help.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!


%22cos%28%221%2F2theta%22%29%22%22%22=%22%22%22%22%2B-+sqrt%28+%281%2Bcos%28theta%29%29%2F2%29+

Since 22.5° is 1%2F2 of 45°, we substitute theta=%2245%B0%22

cos%28%2222.5%B0%22%29%22%22=%22%22%22cos%28%221%2F2%22%22%2A%2245%B0%22%22%29%22%22%22=%22%22%22%22%2B-+sqrt%28+%281%2Bcos%28%2245%B0%22%29%29%2F2%29+

We take the positive result because cos(22.5°) is positive.

cos%28%2222.5%22%29%22%22=%22%22%22%22%2B+sqrt%28+%281%2B%28sqrt%282%29%2F2%29++++%29%2F2%29+

Multiply top and bottom of the complex fraction under the radical by 2:

cos%28%2222.5%22%29%22%22=%22%22sqrt%28+%282%2Bsqrt%282%29%29%2F4%29+

cos%28%2222.5%22%29%22%22=%22%22sqrt%28+2%2Bsqrt%282%29%29%2F2+

That's the final result.  We check it by evaluating that as
.9238795323 with a calculator and then finding the cosine of 22.5° 
and we find that it also has that same decimal value, .9238795323.

Edwin