Correct Answer: Option A

Explanation

Evaluate: \(\frac{cos^2 300º - 4sin^2 120º}{tan^2 135º}\)

Cos 300º = 60º, Sin 120º = 60º, tan 135º = - 45º (using the idea of quadrant}, and the angles are all special.

cos 60º = \(\frac{1}{2}\), sin  60º = \(\frac{\sqrt{3}}{2}\), Tan(-45) = -1

\(\frac{cos^2 300º - 4sin^2 120º}{tan^2 135º}\) =  \(\frac{(\frac{1}{2})^2 - 4(\frac{\sqrt{3}}{2})^2 }{(-1)^2}\)

= \(\frac{\frac{1}{4} - 4\frac{3}{4}}{1}\) = \(\frac{1}{4}\) - 3 = -2\(\frac{3}{4}\)

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