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