A textbook i have states that:
"(sinX)(cosX) = sin(2X)/2"
The book fails to fully explain the derivation of this identity, and I have been unable to figure it out on my own. Any help with this would be much appreciated. Thanks!
2007-02-26 02:37:29 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
I remember its geometrical proof being in one of my books.
Take the general proof, which is the general law:
http://en.wikipedia.org/wiki/Trigonometric_identity#sin.28x_.2B_y.29_.3D_sin.28x.29_cos.28y.29_.2B_cos.28x.29_sin.28y.29
I would suggest the sin(a+b) identity but I thought you would like something else.
2007-02-26 02:44:35 · answer #1 · answered by supersonic332003 7 · 0⤊ 0⤋
sin(2x) = 2 sin x . cosx
[sin(2x)]/2 = (2sinxcosx)/2
since 2/2 is 1 you get (sinx)(cosx)
2007-02-26 03:08:41 · answer #2 · answered by Carla 4 · 0⤊ 0⤋
Do you know the sin addition formula? sin(a + b) = sin(a)cos(b) + cos(a)sin(b). In this case, plug in b = a to get
sin(2a) = sin(a + a) = sin(a)cos(a) + cos(a)sin(a) = 2sin(a)cos(a)
Then divide by 2 to get your identity.
2007-02-26 02:42:58 · answer #3 · answered by sofarsogood 5 · 0⤊ 0⤋