Another Trig Proof...

[HopeWelch]

Is this right? Once again I can only touch the left side of the equation.

[sin(4x)] / 4 = cos^3x sinx - sin^3x cosx

[sin(2x) + sin(2x)] / 4 =

(2sinx cosx + 2sinx cosx) / 4 =

(4sinx cosx) / 4 =

sinx cosx =

Then I multiplied by (sin^2x + cos^2x) / (sin^2x + cos^2x)

because this will give me a 1 in the denominator

Then multiplied out I get:

cos^3x sinx + sin^3x cosx = cos^3x sinx - sin^3x cosx

How do make the left side subtract instead of addition?

 

[pka]

[sin(4x)] / 4 = cos^3x sinx - sin^3x cosx
[sin(2x) + sin(2x)] / 4 =

That is incorrect.
\(\displaystyle \sin(4x)=2\sin(2x)\cos(2x)=4sin(x)cos(x)[\cos^2(x)-\sin^2(x)]\)

 

[HopeWelch]

Thanks...I hate these.