Ask Me Help Desk - Establishing Trigonometric Identity

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.