Prove csc^2 x + sec^2 x = csc^2 x sec^2 xRS shows the 2 sets being multiplied.

csc^2 x + sec^2 x = csc^2 x * sec^2
x

We will start from the left side and prove the right
side.

We know that:

csc(x) =
1/sin(x) ==> csc^2 x = 1/sin^2 x

sec(x) = 1/cos(x)
==> sec^2 x = 1/cos^2 x

We will
substitute:

==> (1/sin^2 x) + (1/cos^2
x)

Now we will rewrite using the common denominator (sin^2
x*cos^2 x)

==> (cos^2 x + sin^2 x) / (sin^2 x* cos^2
x)

Now we know that sin^2 x + cos^2 x =
1

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

==> 1/sin^2 x  *  1/cos^2
x

==> csc^2 x * sec^2 x
...................q.e.d