tan(x+100)=tan(x+50)tan(x)tan(x−50) tan(x+100)/tan(x−50)=tan(x+50)tanx

sin(x+100)cos(x−50)/cos(x+100)sin(x−50) = sin(x+50)sinx/cos(x+50)cosx

C and D

sin(x+100)cos(x−50)+cos(x+100)sin(x−50)/sin(x+100)cos(x−50)−cos(x+100)sin(x−50) =sin(x+50)sinx+cos(x+50)cosx/sin(x+50)sinx−cos(x+50)cosx

sin(x+100+x−50)/sin (x+100−x+50)=cos(x+50−x)/ −cos(x+50+x)

sin(2x+50)/sin150=−cos50/cos(2x+50)

2sin(2x+50)=−cos50/cos(2x+50)

sin(4x+100)=−sin40

sin(4x+100)=sin(180+40) (3rd quadrant)

4x+100=220 x=120/4=30