How can I simplify 1-2*sqrt(x)*sin(sqrt(x))*cos(sqrt(x))?

[Math10]

Homework Statement

How to simplify 1-2*sqrt(x)*sin(sqrt(x))*cos(sqrt(x))?

Homework Equations

None.

The Attempt at a Solution

I know the identity that sin(2x)=2sin(x)cos(x).

 

[Mark44]

Homework Statement

How to simplify 1-2*sqrt(x)*sin(sqrt(x))*cos(sqrt(x))?

Homework Equations

None.

The Attempt at a Solution

I know the identity that sin(2x)=2sin(x)cos(x).

Or sin(2A) = 2sin(A)cos(A).
Let A = $\sqrt{x}$. Can you do something with that?

 

[Math10]

So it's 1-Asin(2A)?

 

[Ray Vickson]

So it's 1-Asin(2A)?

You tell us.

 

[Math10]

1-Asin(2A).

 

[Mark44]

1-Asin(2A).

But what is A? There is no A in the original problem.

 

[Math10]

You said to let A=sqrt(x). See what you posted above.

 

[Mark44]

You said to let A=sqrt(x). See what you posted above.

Right. So now replace A by $\sqrt{x}$.

 

[Math10]

So 1-sqrt(x)*sin(2*sqrt(x)).

 

[Mark44]

So 1-sqrt(x)*sin(2*sqrt(x)).

It's easy enough to check whether this is equal to what you started with.

 

[Math10]

LOL, never mind. I found my mistake in the problem. Thanks for the help.