Using Fourier integral transforms solve the following.

Let be the sine transform of where is the sine transform of and is the cosine transform of .

Suppose that and are odd and even functions respectively.

Show that

Where x' is the derivative of x.

Hk) = S(k).C(k) 04 Sky s(2 Cky / CCC h(x) = _[s(x)[(x+x")=c(x+x")]dx'=-=[c(*)[$(x+x")= s(x-x)]dx* Hk) = S(k).C(k) 04 Sky s(2 Cky / CCC h(x) = _[s(x)[(x+x")=c(x+x")]dx'=-=[c(*)[$(x+x")= s(x-x)]dx*