Question

Evaluate 4 (Sin^4 30°+ Cos^4 60°) - 2/3 (Sin²60° - Cos² 45 ) + 1/2 tan² 60°​

Answer 1

SOLUTION

→ 4 (Sin⁴ 30°+ Cos⁴ 60°) - 2/3 (Sin²60° - Cos² 45 ) + 1/2 tan² 60°

As we know that,

• Sin 30° = ½
• Cos 60° = ½
• Sin 60° = √3/2
• Cos 45° = 1/√2
• Tan 60° = √3

→ 4[(½)⁴ + (½)⁴] - ⅔ [(√3/2)² - (1/√2)²] + ½ × (√3)²

→ 4(1/16 + 1/16) - ⅔(3/4 - 1/2) + 3/2

→ 4 × 2/16 - ⅔(3 - 2/4) + 3/2

→ 8/16 - ⅔ × 1/4 + 3/2

→ 1/2 - 1/6 + 3/2

→ 3 - 1 + 9/6

→ 2 + 9/6

→ 11/6

•°• The value of 4 (Sin⁴ 30°+ Cos⁴ 60°) - 2/3 (Sin²60° - Cos² 45 ) + 1/2 tan² 60° is 11/6