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WAEC Further Mathematics 2024 Paper

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Question : 9

Total: 40

Evaluate:

\frac{\cos^2 300^{\circ} - 4\sin^2 120^{\circ}}{\tan^2 135^{\circ}}

-2 $\frac{3}{4}$
-3 $\frac{3}{4}$
-2 $\frac{1}{4}$
-3 $\frac{1}{4}$

Solution:

Concept:

Use standard trigonometric values for special angles and reference angles from the quadrant.

Explanation:

\cos 300^\circ = \cos(360^\circ - 60^\circ) = \cos 60^\circ = \frac{1}{2}

\sin 120^\circ = \sin(180^\circ - 60^\circ) = \sin 60^\circ = \frac{\sqrt{3}}{2}

\tan 135^\circ = \tan(180^\circ - 45^\circ) = -\tan 45^\circ = -1

Substitute into the expression:

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

= \frac{\frac{1}{4} - 4 \cdot \frac{3}{4}}{1} = \frac{1}{4} - 3 = -\frac{11}{4}

-\frac{11}{4} = -2\frac{3}{4}

Answer:

A.

-2\frac{3}{4}

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