Evaluate the following. 5 cos²120⁰+4sec²30⁰-tan²135⁰ over sin²30⁰+cos²30⁰

Evaluate the following. 5 cos²120⁰+4sec²30⁰-tan²135⁰ over…

Evaluate the following.

${{5 cos^2120⁰+4sec^230⁰-tan^2135⁰} \over sin^230⁰+cos^230⁰}$

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. 67/12.

Numerator:

cos²120° = 0.25 → 5×0.25 = 1.25

sec²30° = 4/3 → 4×4/3 = 16/3

tan²135° = 1

⇒ 1.25 + 16/3 − 1 = 0.25 + 16/3 = 67/12

Denominator:

sin²30° + cos²30° = 0.25 + 0.75 = 1

Final answer = 67/12 ÷ 1 = 67/12