Question

Evaluate the following:

`(sec 70^@)/(cosec 20^@) + (sin 59^@)/(cos 31^@)`

Answer 1

We have to find: `(sec 70^@)/(cosec 20^@) + (sin 59^@)/(cos 31^@)`

Since `sec 70^@/(cosec 20^@) + sin 59^@/cos 31^@` and `sec (90^@ - theta) = cosec theta

So

`sec 70^@/(cosec 20^@) + sin 59^@/cos 31^@ = (sec (90^@ - 20^@))/(cosec 20^@) + (sin (90^@ - 31^@))/(cos 31^@)` 

`= (cosec 20^@)/(cosec 20^@) + (cos 31^@)/(cos 31^@)`

 1 + 1

= 2

So value of `(sec 70^@)/(cosec 20^@) + (sin 59^@)/(cos 31^@)` is 2