Given that sin (5x - 28)o = cos (3x - 50)o,0 o, find the value of x
A
14o
B
21o
C
32o
D
39o
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
Sin (5x – 28)o = cos (3x - 50)o
Since by the trigonometry relation
Sin(5x – 28)o = cos[90 – (5x – 28)]o
Hence cos(3x – 50)o = cos[90 – (5x – 28)]o
3x – 50 = 90 - (5x-28)
3x – 50 = 90 – 5x + 28
3x + 5x = 90 + 28 + 50
8x = 168
\(x = \frac{168}{8}=21^{\circ}\)
Source: Myschool Past Questions Archive (Record #26619)