3tan²30° + (1/4)sec60° + 5cot²45° - (2/3)sin²60° এর মান কত?
Solution
Correct Answer: Option A
3tan230° + (1/4)sec60° + 5cot245° - (2/3)sin260°
= 3(tan30°)2 + (1/4)sec(60°) + 5(cot45°)2 - (2/3)(sin60°)2
= 3 × (1/√3)2 + (1/4) × 2 + 5 × (1)2 - (2/3) × (√3/2)2
= (3 × 1/3) + (1/2) + 5 - (2/3 × 3/4)
= 1 + 1/2 + 5 - 1/2
= (2 + 1 + 10 - 1)/2
= 12/2
= 6
= 3(tan30°)2 + (1/4)sec(60°) + 5(cot45°)2 - (2/3)(sin60°)2
= 3 × (1/√3)2 + (1/4) × 2 + 5 × (1)2 - (2/3) × (√3/2)2
= (3 × 1/3) + (1/2) + 5 - (2/3 × 3/4)
= 1 + 1/2 + 5 - 1/2
= (2 + 1 + 10 - 1)/2
= 12/2
= 6
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