Why does sin(t)cos(t) = x(1-x)^{1/2}

[laura_a]

I'm working on a differential equation, and my answer is

sin(t)cos(t) which in the text, they jump from that straight to
$$x(1-x^2)^{\frac{1}{2}}$$

I've forgotten a lot of what I learned in my first few years of Uni and I just can't remember why they equal, I thouht it might be an identity, but I have looked on the net and can't find one... can someone please shed some light? Thanks

 

[laura_a]

Dont worry I worked it out

 

[George Jones]

I'm working on a differential equation, and my answer is

sin(t)cos(t) which in the text, they jump from that straight to
$$x(1-x^2)^{\frac{1}{2}}$$

I've forgotten a lot of what I learned in my first few years of Uni and I just can't remember why they equal, I thouht it might be an identity, but I have looked on the net and can't find one... can someone please shed some light? Thanks

What is $x$?

 

[theneedtoknow]

was there a u-substitution or something earlier on? cause taking either sin(t) as x, or cos(t) as x, would give the second equation when rewritten in terms of x.