Question

Evaluate without using a trigonometric table:

`(2 tan 36°)/(cot 54°) + (3 cot 38°)/(tan 52°) − (2 sec 41°)/("cosec" 49°)` 

Answer 1

Use co-function identities:

`cot(90° −  θ) = tan θ, tan(90° −  θ) = cot θ, "cosec"(90° −  θ) = sec θ.`

`(2 tan 36°)/(cot 54°) = (2 tan 36°)/(tan 36°) = 2`

`(3 cot 38°)/(tan 52°) = (3 cot 38°)/(cot 38°) = 3`

`(2 sec 41°)/("cosec"  49°) = (2 sec 41°)/(sec 41°) = 2`

2 + 3 − 2   ...[Adding]

= 3