Question
Download Solution PDFWhat is the value of 5√3 cos 60° tan 30° - 3 cos 0° + 3 cos2 45° + 2 sin2 60°?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used:
Cos 60° = 1/2; tan 30° = 1/√3;
cos 45° = 1/√2; sin 60° = √3/2
Calculation:
5√3 cos 60° tan 30° - 3 cos 0° + 3 cos2 45° + 2 sin2 60°
⇒ 5√3 × (1/2) × (1/√3) - 3 × 1 + 3 × (1/√2)2 + 2 × (√3/2)2
⇒ 5√3 × (1/2) × (1/√3) - 3 + 3/2 + 3/2
⇒ 5/2 - 3 + 3/2 + 3/2
⇒ 2.5 - 3 + 3
⇒ 2.5
∴ The correct answer is 2.5.
Last updated on Jul 12, 2025
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