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\(^o\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
Sin(5x - 28) = Cos(3x - 50)………..i
But Sin\alpha = Cos(90 - \alpha)
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
Source: Myschool Past Questions Archive (Record #47576)