I'm having trouble solving this problem...
sec(x+y)=sec(x)sec(y)/1-tan(x)tan(y)

What is sec(x+y) ?

Convert into cos:

sec(x+y) = \frac{1}{cos(x+y)}

Then, apply the compound angle formula:

cos(x+y) = cos(x)cos(y) - sin(x)sin(y)

Replace that in the previous expression:

\frac{1}{cos(x+y)} = \frac{1}{cos(x)cos(y) - sin(x)sin(y)}

Now, use something similar to rationalisation, but with a specific function.

\frac{1}{cos(x)cos(y) - sin(x)sin(y)} = \frac{1}{cos(x)cos(y) - sin(x)sin(y)} \times \frac{\frac{1}{cos(x)cos(y)}}{\frac{1}{cos(x)cos(y )}}

Let's see where it goes.