The value of (5 cos² 60ᵒ + 4 sec² 30ᵒ -tan² 45ᵒ)/(tan² 60ᵒ - sin² 30ᵒ - cos² 45ᵒ) is:

The value of (5 cos² 60ᵒ + 4 sec² 30ᵒ -tan² 45ᵒ)/(tan² 60ᵒ…

The value of $\frac{5 cos^2 60^o + 4 sec^2 30^o -tan^2 45^o}{tan^2 60^o - sin^2 30^o - cos^2 45^o}$ is:

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Correct answer: A

Explanation

The correct answer is option 1 i.e. $\frac{67}{27}$

One can solve this question by directly placing the values of trigonometric ratios.

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

= (5/4 + 16/3 - 1)/( 18/8)

= (67/12)/(18/8)

= 67/27.