Question

Evaluate the following without using a table:

`2 (tan 32°)/(cot 58°) + (sec 46°)/("cosec" 44°)`

Answer 1

Given:

`2 (tan 32°)/(cot 58°) + (sec 46°)/("cosec" 44°)`

Step 1:

cot(90° − θ) = tan θ and cosec(90° − θ) = sec θ

Since 58° = 90° − 32°

cot 58° = tan 32°

`(tan 32°)/(cot 58°)` = 1 

so 2 × 1 = 2     ...[(i)]

Step 2:

44° = 90° − 46°, cosec 44° = sec 46°

`(sec 46°)/("cosec" 44°)` = 1     ...[(ii)]

= 2 + 1    ...[Adding (i) & (ii)]

= 3