(i)  cos 48° – sin 42°      

(ii)  cosec 31° – sec 59°

Solutions:

(i) cos 48° – sin 42°

In order to simplify this, we need to convert the cos function into sin function

We all know that, 48° is written as 90° – 42°, which equals to the sin 42°.

= cos (90° – 42°) – sin 42°

Substituting the values to simplify this equation

= sin 42° – sin 42° = 0

(ii) cosec 31° – sec 59°

In order to simplify this, we need to convert the cosec function into sec function

We all know that, 31° is written as 90° – 59°, which equals to the sec 59°

= cosec (90° – 59°) – sec 59°

Substituting the values to simplify this equation

= sec 59° – sec 59° = 0