Answer:
The correct option is C.
Step-by-step explanation:
Given information: Angles α and β are the two acute angles , β > ∝.
Given equation is
[tex]\sin(\frac{x}{2}+20x)=\cos (2x+\frac{15x}{2})[/tex]
[tex]\cos(90-(\frac{x}{2}+20x))=\cos (2x+\frac{15x}{2})[/tex] [tex][\because \sin (90-x)=\cos x][/tex]
Equating both the sides.
[tex]90-\frac{x}{2}-20x=2x+\frac{15x}{2}[/tex]
[tex]90=2x+\frac{15x}{2}+\frac{x}{2}+20x[/tex]
[tex]90=22x+\frac{16x}{2}[/tex]
[tex]90=22x+8x[/tex]
[tex]90=30x[/tex]
[tex]x=3[/tex]
The value of angles is
[tex]\frac{x}{2}+20x=\frac{3}{2}+20(3)=1.5+60=61.5[/tex]
[tex]2x+\frac{15x}{2}=2(3)+\frac{15(3)}{2}=6+22.5=28.5[/tex]
Since 61.5>28.5, therefore the value of β is 61.5. Option C is correct.
