Find the value of a in the equation: cos (a + 14)° = sin (4a
MATHEMATICS
WAEC 2023
Find the value of a in the equation: cos (a + 14)° = sin (4a + 6)°
Explanation
cos (a + 14)° = sin (4a + 6)°
Recall, cos θ = sin (90 - θ)
⇒ sin (90 - (a + 14)) = sin (4a + 6)
⇒ sin (90 - a - 14) = sin (4a + 6)
⇒ sin (76 - a) = sin (4a + 6)
⇒ 76 - a = 4a + 6
⇒ 76 - 6 = 4a + a
⇒ 70 = 5a
\(a = \frac{70}{5}\)
therefore, a = 14
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