Solving this trig identity??

[TheNascar92]

I have this identity:

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

The farthest i have gotten so far is using the double angle formula to rewrite the sin2x and get:

2sinxcos^2x-2sinx

Im lost as to what i should do from here if anyone can help it would be appreciated thanks

 

[Mrspi]

I have this identity:

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

The farthest i have gotten so far is using the double angle formula to rewrite the sin2x and get:

2sinxcos^2x-2sinx

Im lost as to what i should do from here if anyone can help it would be appreciated thanks

What you've done so far is fine.

Now, you have this:

2 sin x cos^2 x - 2 sin x

Remove a common factor of -2 sin x from both terms:

-2 sin x (1 - cos^2 x)
Now...look at the Pythagorean identities. What is 1 - cos^2 x?