Question

Evaluate : 4 (sin² 60° + cos⁴ 30°) - 3 (tan² 60° - tan² 45°) 5 cos² 45°

Answer 1

Given:

4 (sin² 60° + cos⁴ 30°) - 3 (tan² 60° - tan² 45°) 5 cos² 45°

= 4 ((√3/2)⁴ + (√3/2)⁴) - 3 ((√3)² - 1²) 5 (1/√2)²

= 4 (9/16) + (9/16) - 3(3-1) + 5 ×1/2

= 4 ((9+9)/16) - 3 × 2 + 5/2

= 4 × (18/16) - 6 + 5/2

= (18/4) - 6 + 5/2

= 9/2 - 6 + 5/2

= 9/2 + 5/2 - 6

= (9+5)/2 - 6

= 14/2 - 6

= 7 - 6

= 1

Hence,

4 (sin² 60° + cos⁴ 30°) - 3 (tan² 60° - tan² 45°) 5 cos² 45° = 1. Ans.