To find the maximum value of the expression 12sin‌x−5‌cos‌x+3, we start by considering the form asin‌x+b‌cos‌x, which achieves its maximum value at √a2+b2. For our specific expression, we have a=12 and b=−5. The calculation for the maximum value of 12sin‌x−5‌cos‌x is: √122+(−5)2=√144+25=√169=13 Therefore, the maximum value of the entire expression 12sin‌x−5‌cos‌x+3 is: 13+3=16