# Verifying a trig identity

• Oct 22nd 2009, 04:50 PM
nascar77
Verifying a trig identity
I am having some trouble verifying this identity ive tried several ways to solve it but for some reason i cant get the right answer it is:

sin(2x)cosx-2sinx=-2sin^3x

the last part reads "negative sine cubed x" ive tried factoring and the double angle formula but nothing seems to work if anyone has any idea to help id appreciate thanks
• Oct 22nd 2009, 05:02 PM
skeeter
Quote:

Originally Posted by nascar77
I am having some trouble verifying this identity ive tried several ways to solve it but for some reason i cant get the right answer it is:

sin(2x)cosx-2sinx=-2sin^3x

the last part reads "negative sine cubed x" ive tried factoring and the double angle formula but nothing seems to work if anyone has any idea to help id appreciate thanks

$\displaystyle \sin(2x)\cos{x} - 2\sin{x}$

$\displaystyle 2\sin{x}\cos^2{x} - 2\sin{x}$

$\displaystyle 2\sin{x}(\cos^2{x} - 1)$

$\displaystyle -2\sin{x}(1 - \cos^2{x})$

$\displaystyle -2\sin{x}(\sin^2{x})$

$\displaystyle -2\sin^3{x}$