Question

Evaluate.

5 cos²60° + 4sec²30° - tan²45° / sin²30° + cos²30°

Answer 1

Answer:

10/3

Step-by-step explanation:                         using BODMAS rule

  5cos²60° + 4sec²30° - tan²45°/sin²30° + cos²30°

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

= 5/4 + 16/3 - 4 + 3/4

= 2-4 +16/3

= (-6+16)/3

= 10/3

Answer 2

Using trigonometric table, we know that

Cos60° = 1/2

Sec30° = 2/√3

Tan45 = 1

Sin30 = 1/2

Cos30 = √3/2

---------------------------

Substituting the values

→ 5(1/2)² + 4(2/√3)² - (1)² / (1/2)² + (√3/2)²

→ 5 x 1/4 + 4 x 4/3 - 1 / 1/4 + 3/4

→ 5/4 + 16/3 - 1 / 4/4

→ 5/4 + 16/3 - 1

→ 15/12 + 64/12 - 1

→ 79/12 - 1

→ 79 - 12 / 12

→ 67/12