Question

Evaluate the following without using a table:

`(tan 36°)/(cot 54°)` + sin 26° sec 64°

Answer 1

Given:

`(tan 36°)/(cot 54°)` + sin 26° sec 64°

Step 1:

`(tan 36°)/(cot 54°)`

cot 54° = `1/(tan 54°)`

tan 36° = cot 54° tan A = cot(90° − A)

`(tan 36°)/(cot 54°) + ((tan 36°)/1)/(tan 54°) = tan 36° ⋅ tan 54°`

tan 36° ⋅ tan 54° = 

`(tan 36°)/(cot 54°) = 1`     ...(i)

Step 2: 

sec 64° = `1/(cos 64°)`

cos 64° = sin 26°

sec 64° = `1/(sin 26°)`

sin 26° ⋅ sec 64°

= sin 26° ⋅ `1/(sin 26°)` = 1     ...(ii)

= 1 + 1    ...[Adding (i) & (ii)]

= 2