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WAEC Mathematics 2023 Paper

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Question : 19

Total: 50

Find the value of a in the equation: cos (a + 14)° = sin (4a + 6)°

15
17
14
21

Solution:

Concept:

Use the complementary angle identity:

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

.

Explanation:

Given:

\cos(a + 14)^\circ = \sin(4a + 6)^\circ

Rewrite

\cos(a + 14)^\circ

as

\sin\left(90^\circ - (a + 14)^\circ\right)

.

So,

\sin(76 - a)^\circ = \sin(4a + 6)^\circ

.

Equating the angles:

76 - a = 4a + 6

.

Simplify:

76 - 6 = 4a + a

.

Thus,

70 = 5a

.

Therefore,

a = \frac{70}{5} = 14

.

Answer:

a = 14

Correct option: C. 14.

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