Posted by Sarah on Wednesday, May 26, 2010 at 9:39pm.
if A+B+C=180degrees, prove that 2sin(B+C)sinA=1cos2A

math  Reiny, Wednesday, May 26, 2010 at 9:55pm
OK, B+C = 180A
so
LS = 2sin(B+C)sinA
= 2sin(180  A)sinA
= 2(sinA)sinA
= 2 sin^2 A
RS = 1  cos 2A
= 1 (2sin^2 A  1)
= 2sin^2 A
= LS

math  Mike, Wednesday, May 26, 2010 at 10:00pm
in part 1, how does sin(180A) equal sinA from line 45

Mike you are right  math  Reiny, Wednesday, May 26, 2010 at 10:12pm
Actually I have 2 errors in my solution
1.
sin(180A) = sinA , not sinA
e.g. sin (150) = sin(180150) = sin 30
2. cos 2A = 1  2sin^2 A, I had it backwards
so here is the correct solution
LS = 2sin(B+C)sinA
= 2sin(180  A)sinA
= 2(sinA)sinA
= 2 sin^2 A
RS = 1  cos 2A
= 1 (1  2sin^2 A)
= 2sin^2 A
= LS
sorry about that
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