Question

Evaluate the following:

`(sec 48^circ)/("cosec"  42^circ)`

Answer 1

Given: `(sec 48^circ)/("cosec"  42^circ)`

48° = 90° – 42° 

So, sec 48° = sec (90° – 42°) 

= `1/cos(90^circ - 42^circ)` 

= `1/(sin 42^circ)` 

= cosec 42° 

Therefore, `(sec 48^circ)/("cosec"  42^circ)`

= `("cosec"  42^circ)/("cosec"  42^circ)`

= 1