Given that Sin (5\(_x\) − 28)\(^o\) = Cos(3\(_x\) − 50)\(^o\), O\(_x\) < 90\(^o\)
Find the value of x
A. 14\(^o\)
B. 21\(^o\)
C. 32\(^o\)
D. 39\(^o\)
Correct Answer: B
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 = \(\frac{168}{8}\)
x = 21\(^o\)
Answer is B
