Homework Help: math

Posted by Sarah on Wednesday, May 26, 2010 at 9:39pm.

if A+B+C=180degrees, prove that 2sin(B+C)sinA=1-cos2A

math - Reiny, Wednesday, May 26, 2010 at 9:55pm
OK, B+C = 180-A
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(180-A) equal -sinA from line 4-5
Mike you are right - math - Reiny, Wednesday, May 26, 2010 at 10:12pm
Actually I have 2 errors in my solution

1.
sin(180-A) = sinA , not -sinA

e.g. sin (150) = sin(180-150) = 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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