SOLUTION: 2 sin 112.5° cos 112.5°=?

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Question 1047986: 2 sin 112.5° cos 112.5°=?
Found 2 solutions by advanced_Learner, ikleyn:
Answer by advanced_Learner(501) About Me  (Show Source):
You can put this solution on YOUR website!
the answer is -1

Answer by ikleyn(52905) About Me  (Show Source):
You can put this solution on YOUR website!
.
2 sin 112.5° cos 112.5°=?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

2sin%28alpha%29%2Acos%28alpha%29 = sin%282alpha%29

is well known trigonometry formula (see the lesson Trigonometric functions of multiply argument in this site, for example).


Therefore,

2 sin 112.5° cos 112.5°= = sin(2*112.5°) = sin(225°) = -sqrt%282%29%2F2.


Answer.  2 sin 112.5° cos 112.5° = -sqrt%282%29%2F2.