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WAEC Mathematics 2025 Paper

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Question : 46

Total: 50

Without using tables, find the value of:

\frac{sin 20°}{cos 70°} + \frac{cos 25°}{sin 65°}

2
0
1
-1

Solution:

Concept:

Complementary angle identities:

\sin x = \cos(90^\circ - x)

and

\cos x = \sin(90^\circ - x)

.

Explanation:

First, rewrite each denominator using complementary angles.

\cos 70^\circ = \sin(90^\circ - 70^\circ) = \sin 20^\circ

\sin 65^\circ = \cos(90^\circ - 65^\circ) = \cos 25^\circ

Now substitute into the given expression:

\frac{\sin 20^\circ}{\cos 70^\circ} + \frac{\cos 25^\circ}{\sin 65^\circ} = \frac{\sin 20^\circ}{\sin 20^\circ} + \frac{\cos 25^\circ}{\cos 25^\circ}

Each fraction simplifies to

1

:

1 + 1 = 2

Answer:

2

(Option A)

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