sin(X)sec(x)=1-(cos^2)x/sin(X)cos(X)

You need the following two identities for this problem:

sec(x) = 1/cos(x)

sin

^{2}x + cos^{2}x = 1Now let's use them in your problem:

sin(x)sec(x) = [1-cos

^{2}(x)]/sin(x)cos(x)sin(x)/cos(x) = sin

^{2}(x)/sin(x)cos(x) [sec(x) = 1/cos(x), 1-cos^{2}(x)=sin^{2}(x)]sin(x)/cos(x) = sin(x)/cos(x)

QED