2018
Mathematics
67ca00ce0c643c71d77dee1f
Given that Sin (5x − 28)° = Cos(3x − 50)°, 0 < x < 90° Find the value °f x
A.
14°
B.
21°
C.
32°
D.
39°
Correct Answer: 21°
Explanation
Sin(5x - 28) = Cos(3x - 50)………..i But Sinα = Cos(90 - α) So Sin(5x - 28) = Cos(90 - [5x - 28]) Sin(5x - 28) = Cos(90 - 5x + 28) Sin(5x - 28) = Cos(118 - 5x)………ii Combining i and ii Cos(3x - 50) = Cos(118 - 5x) 3x - 50 = 118 - 5x Collecting the like terms 3x + 5x = 118 + 50 8x = 168 x = 168/8 x = 21°
Sin(5x - 28) = Cos(3x - 50)………..i But Sinα = Cos(90 - α) So Sin(5x - 28) = Cos(90 - [5x - 28]) Sin(5x - 28) = Cos(90 - 5x + 28) Sin(5x - 28) = Cos(118 - 5x)………ii Combining i and ii Cos(3x - 50) = Cos(118 - 5x) 3x - 50 = 118 - 5x Collecting the like terms 3x + 5x = 118 + 50 8x = 168 x = 168/8 x = 21°THIS WEEK's
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