Question

1. Buktikan bahwa tan(45°+x)•tan(135°+x)= -1
2. Sederhanakan Sin123°cos57° + cos123°sin57°
3. Cos80°cos10° - sin80°cos10°

Dibantu ya

Answer 1

Sin(45+x)/cos(45+x)*sin(135+x)/cos(135+x)
=sin(45+x)*sin(135+x)/[cos(45+x)*cos(135+x)]
=[-1/2*(cos(180+2x)-cos(90))] / [1/2*(cos(180+2x)+cos(90))]
=-1*(-cos(2x))/(-cos(2x))
=-1

2. sin(123)cos(57)+cos(123)sin(57)=sin(123+57)=sin(180)=0

3.cos(80)cos(10)-sin(80)sin(10)=cos(80+10)=cos(90)=0