Question

Evaluate without using a trigonometric table:

Cos 20° cosec 70° + `(tan⁡34°)/(cot⁡56°)`

Answer 1

Given:

cos 20° ⋅ cosec 70° + `(tan⁡34°)/(cot⁡56°)`

Step 1: cosec 70° = `1/(sin 70°) and sin 70° = cos 20°`

cos 20° ⋅ cosec 70° = cos 20° ⋅ `1/(cos 20°) = 1`

Step 2:

cot 56° = tan(90° − 56°) = tan 34°

`(tan 34°)/(cot 56°) = (tan 34°)/(tan 34°)` = 1

= 1 + 1    ...[Adding]

= 2