Answer:
The correct option is D) [tex]x=11.75[/tex]
Step-by-step explanation:
We need to find out the value of x in the provided function;
[tex]\cos (2x-4)= \sin (6x)[/tex] .......(1)
Since, [tex]\cos (90-\theta)= \sin \theta[/tex]
So, we can replace [tex]\sin (6x)= \cos (90-\theta)[/tex] in equation(1)
[tex]\cos (2x-4)= \sin (6x)[/tex]
[tex]\cos (2x-4)=\cos (90-6x)[/tex]
comparing the trigonometric ratio
so,
[tex]2x-4=90-6x[/tex]
add both the sides by 6x,
[tex]2x-4+6x=90[/tex]
[tex]8x-4=90[/tex]
add both the sides by 4,
[tex]8x=94[/tex]
Divide both the sides by 8,
[tex]x=\frac{94}{8}[/tex]
[tex]x=11.75[/tex]
Therefore, the correct option is D) [tex]x=11.75[/tex]
