# trig - prove identities

• November 4th 2008, 11:47 AM
getem j
trig - prove identities
prove so L.S. = R.S.
sin8A = 8sinAcosAcos2Acos4A

thanks
• November 4th 2008, 11:59 AM
Soroban
Hello, getem j!

We're expected to know this identity: . $\sin2\theta \:=\:2\cdot\sin\theta\cdot\cos\theta$

Quote:

Prove: . $\sin8A \:= \:8\cdot\sin A\cdot\cos A\cdot\cos2A\cdot\cos4A$

We have: . $\sin8A \;=\;2\cdot\underbrace{\sin4A}\cdot\cos4A$

. . . . . . . . . $=\; 2\overbrace{(2\cdot\sin2A\cdot\cos2A)}\cdot\cos4A$

. . . . . . . . . $=\;4\cdot\underbrace{\sin2A}\cdot\cos2A\cdot\cos4A$

. . . . . . $= \;4\cdot\overbrace{(2\cdot\sin A\cdot\cos A)}\cdot\cos2A\cdot\cos4A$

. . . . . . $= \;8\cdot\sin A\cdot\cos A\cdot\cos2A\cdot\cos4A$

• November 4th 2008, 12:11 PM
getem j
wow thank you so much , your a life saver