Answer:
x=13.14
Step-by-step explanation:
The given equation is:
[tex] \sin \: (2x + 1) = \cos (5x - 3)[/tex]
Recall that, the sine and cosine functions are complementary functions.
Therefore:
[tex] \sin(2x + 1) = \cos \: (90 - 2x - 1)[/tex]
This means that:
[tex]\sin(2x + 1) = \cos \: (5x - 3) \\ \implies \cos \: (90 - 2x - 1) = \cos(5x - 3)[/tex]
This means that:
[tex]90 - 2x - 1 = 5x - 3[/tex]
Combine like terms:.
[tex]90 -1 + 3 = 5x + 2x[/tex]
[tex]92 =7 x[/tex]
[tex]x = \frac{92}{7} [/tex]
x=13.14
