Question

Evaluate without using a trigonometric table:

`(3 sin 32°)/(cos 58°) + (4 tan 46°)/(cot 44°) − (5 sec 62°)/("cosec" 28°)`

Answer 1

Use co-function identities:

cos 58° = sin 32° 

= `(3 sin 32°)/(cos 58°) = 3`

cot 44° = tan(90° − 44°) = tan 46°

= `(4 tan 46°)/(cot 44°) = 4`

sec 62° = `1/(cos 62°) = 1/(sin 28°) = "cosec" 28°`

= `(5 sec 62°)/("cosec" 28°)` = 5

= 3 + 4 − 5    ...[expression equals]

= 2