Question

Find the value of

[tan60°cosec30° + tan30°sec60°]/[sin²60° + 2cot²45° - sec²30°]

1. (16√3)/7
2. (32√3)/17
3. (32√3)/7
4. (16√3)/17

Answer 1

Correct Answer - Option 2 : (32√3)/17

Calculation: 

[tan60°cosec30° + tan30°sec60°]/[sin260° + 2cot245° - sec230°]

⇒ [(√3 × 2) + (1/√3 × 2)]/[(√3/2)² + (2 × 1) - (2/√3)²]

⇒ [(2√3 + 2/√3)]/[3/4 + 2 - 4/3]

⇒ (6 + 2)/(17√3/12)

⇒ (8 × 12)/17√3

⇒ 32√3/17

∴ The required value is (32√3)/17.