Angles α and β are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of α if α < β. sin(2x − 8) = cos(6x − 6)

Answer:The value of angle α is 18 degree.Step-by-step explanation:Given information: Angles α and β are the two acute angles , α < β.Given equation is[tex]\sin (2x-8)=\cos (6x-6)[/tex][tex]\cos (90-(2x-8))=\cos (6x-6)[/tex]        [tex][\because \sin (90-x)=\cos x][/tex]Equating both sides.[tex]90-2x+8=6x-6[/tex][tex]98+6=6x+2x[/tex][tex]104=8x[/tex][tex]13=x[/tex]The value of x is 13.The measure of angles is[tex]2x-8=2(13)-8=18[/tex][tex]6x-6=6(13)-6=72[/tex]Since 18<72, therefore the value of angle α is 18 degree.