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

Algebra.Com
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)   (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  then  

Let A = 30°, B = 45°, C = -60°



}}}
 
 

But:


 
 






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

RELATED QUESTIONS

If cos(A-B)+cos(B-C)+cos(C-A)= -3/2, prove that:... (answered by robertb)
prove that... (answered by Fombitz)
given that sin A = 1 - sqrt(2) show that cos^2A +2SinA =... (answered by jim_thompson5910,lwsshak3)
If A + B + C = 180 then prove that Cos^2 A + cos^2 B + 2cosAcosBcosC=sin^2... (answered by robertb)
If A, B, C are angles of a triangle, prove that cosA + cosB + cosC =... (answered by MathLover1)
Find the exact value of sin 120°. A sin = sqrt3/2 B sin = -sqrt3/2 C sin =... (answered by jim_thompson5910)
If A+B+C=π then establish the given relation (sin2A+sin2B+sin2C)/(4cosA/2 cosB/2... (answered by robertb)
Prove that: (sin a cos b+cos a sin b)^2+(cos a cos b-sin a sin b)^2 =... (answered by solver91311)
After transformations, the expression sin (A + B)sin (A - B) can be proved to be equal... (answered by ikleyn,math_tutor2020)