Express 6*(sin x)*(cos x) as a single sine or cosine function.

The question put is to express the 6sinxcosx as the function of
single sine of cosine function.

  As it is, the the given finction
a single function with both sinx and cosx. f(x) = 6sinxcosx.

We can
rewrite the function as a function of  sinx as below:

f(sinx) = 6
sinx(1-sin^2x)^(1/2), as cosx = (1-sin^2x).

We can write the
function purely as a function of  K*sinX  as below:

6sinxcosx =  3
(2sinxcosx) = 3sin(2x)

6 sinxcosx = 3sin(2x) , as  sin2x= sin(x+x) =
sinxcosx+cosxsinx = 2sinxcosx.

We can write 6sinxcosx =  sin(2x) =
cos(90-2x)

We cane write the  6sinxcosx =
6cosx*(1-cos2^)^(1/2).