Question

4tan²60+5sin³30+cos²45/tan²45+2sin30 × cos 60

Answer 1

Answer:

13.625

Step-by-step explanation:

tan 60° =√3

∴ tan²60° = (√3)²=3

⇒4 tan²60°= 4*3=12

sin 30°=1/2

⇒5 sin³30°=5* (1/2)³

               = 5* 1/8   = 5/8

2 sin 30°=1

cos 45°=1/√2

⇒cos²45° = 1/2

tan 45°=1

⇒tan²45°=1

cos 60°=1/2

∴4 tan²60+5 sin³30+cos²45/tan²45+2 sin 30 × cos 60

= 12+5/8+(1/2)/1+1*1/2

= 12+5/8+1/2+1/2

=13+5/8 =13.625

Answer 2

Solution:

We know that,

tan60° = √3

sin30° = 1/2

cos45° = 1/√2

tan45° = 1

cos60° = 1/2

∴ (4 tan²60° + 5 sin³30° + cos²45°) / (tan²45° + 2 sin30° × cos60°)

= {4 (√3)² + 5 (1/2)³ + (1/√2)²} / {(1)² + 2 (1/2) × 1/2}

= {(4 × 3) + (5 / 8) + (1 / 2)} / {1 + (2 / 2) × (1 / 2)}

= (12 + 5/8 + 1/2) / (1 + 1 × 1/2)

= {(96 + 5 + 4)/8} / (1 + 1/2)

= 105/8 * 3/2

= 315/16

Or,

4 tan²60° + 5 sin³30° + cos²45° / tan²45° + 2 sin30° × cos60°

= 4 (√3)² + 5 (1/2)³ + (1/√2)² / (1)² + 2 (1/2) × (1/2)

= 12 + 5/8 + (1/2) / 1 + 1 × 1/2

= 12 + 5/8 + 1/2 + 1 × 1/2

= 12 + 5/8 + 1/2 + 1/2

= 12 + 5/8 + 1

= (96 + 5 + 8)/8

= 109/8