Prove sin x tan x = sec x - cos x

sin(x)*tan(x) = sec(x) -
cos(x)

We will start from the left
side.

==> We know that tan(x) =
sin(x)/cos(x)

==> sin(x)*tan(x) = sin(x)*sin(x)/
cos(x)

                             = sin^2 x/
cos(x)

But we know that sin^2 x = 1- cos^2
x

==> sin(x)*tan(x) = (1-cos^2 x) /
cosx

                             = 1/cos(x)  - cos^2 x /
cosx

But 1/cosx =
sec(x)

==> sin(x)*tan(x) = sec(x) -
cos(x).........q.e.d