3tan²30° + (1/4)sec60° + 7cot²45° - (2/3)sin²60° এর মান কত?

প্রশ্ন: 3tan²30° + (1/4)sec60° + 7cot²45° - (2/3)sin²60° এর মান কত?

সমাধান:
3tan²30° + (1/4)sec60° + 7cot²45° - (2/3)sin²60°
= 3(tan30°)² + (1/4)sec(60°) + 7(cot45°)² - (2/3)(sin60°)²
= 3 × (1/√3)² + (1/4) × 2 + 7 × (1)² - (2/3) × (√3/2)²
= (3 × 1/3) + (1/2) + 7 - (2/3) × (3/4)
= 1 + 1/2 + 7 - 1/2
= 8