Given that sin (5x x − 28)o o = cos(3x x − 50)o o , Ox x < 90o o Find the value of x

Given that sin (5$x$ − 28)${}^o$ = cos(3$x$ − 50)${}^o$, O$x$ < 90${}^o$

Find the value of $x$

Answer Details

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${}^o$