Posted by Sarah on .
if A+B+C=180degrees, prove that 2sin(B+C)sinA=1cos2A

math 
Reiny,
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,
in part 1, how does sin(180A) equal sinA from line 45

Mike you are right  math 
Reiny,
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