SOLUTION: If 2(A+B+C)=A Prove that Sin^2 A + Sin^2 B + Sin^2 C= 1-2sinA.sinB.sinC

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Question 1068474: If 2(A+B+C)=A Prove that
Sin^2 A + Sin^2 B + Sin^2 C= 1-2sinA.sinB.sinC
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Sorry but that is not true. Maybe you copied it wrong.

Here is a counterexample to disprove this: 

If 2%28A%2BB%2BC%29=A then sin%5E2%28A%29+%2B+sin%5E2%28B%29+%2B+sin%5E2%28C%29%22%22=%22%221-2sin%28A%29%2Asin%28B%29%2Asin%28C%29 

Let A = 30°, B = 45°, C = -60°

2%28A%2BB%2BC%29%22%22=%22%22A
2%28%2230%B0%22%2B%2245%B0%22%2B%22%28-60%29%B0%22%29%5E%22%22%29%22%22=%22%22%2230%B0%22
2%28%2230%B0%22%2B%2245%B0%22-%2260%B0%22%29}}}%22%22=%22%22%2230%B0%22
2%28%2215%B0%22%29%22%22=%22%22%2230%B0%22 
%2230%B0%22%22%22=%22%22%2230%B0%22 

But:
sin%5E2%28%2230%B0%22%29+%2B+sin%5E2%28%2245%B0%22%29+%2B+sin%5E2%28%22-60%B0%22%29%22%22=%22%221-2sin%28%2230%B0%22%29%2Asin%28%2245%B0%22%29%2Asin%28%22-60%B0%22%29

%281%2F2%29%5E2%2B%28sqrt%282%29%2F2%29%5E2%2B%28-sqrt%283%29%2F2%29%5E2%22%22=%22%221-2%281%2F2%29%28sqrt%282%29%2F2%29%28-sqrt%283%29%2F3%29 
 
1%2F4%2B2%2F4%2B3%2F4%22%22=%22%221-2%281%2F2%29%28sqrt%282%29%2F2%29%28-sqrt%283%29%2F2%29

6%2F4%22%22=%22%221%2Bsqrt%286%29%2F4

3%2F2%22%22=%22%221%2Bsqrt%286%29%2F4

which is false, so we cannot prove something that is false.
If you did not copy it wrong, then be sure to tell your teacher.
If you copied it wrong, you can put the correct identity in the
thank-you note form below.  I will get back to you by email.

Edwin