Step-by-step explanation:
Assume 80° should be 180° to have same pattern.
Use reduction formulas and solve:
- [tex]\dfrac{sin(180+A)+2cos(180+A)cos(A-180)}{2cos^2(360+A)-cos(-A)} =[/tex]
- [tex]\dfrac{-sin(A)+2(-cos(A))(-cos(A))}{2cos^2(A)-cos(A)} =[/tex]
- [tex]\dfrac{2cos^2(A)-sin(A)}{2cos^2(A)-cos(A)}[/tex]
As given, it simplifies to the above fraction.
If the sin was cos then the final result would be 1 as both numerator and denominator would be equal.
