Prove that: `cos((3pi)/2+x)cos(2pi+x){cot((3pi)/2-x)+"cot"(2pi+x)}=1`

Prove that: cos((3 pi)/(2)+x)cos(2pi+x)[cot((3 pi)/(2)-x)+cot(2 pi+x)]=1

Prove that: cos((3 pi)/(2)+x)cos(2 pi+x){cot((3 pi)/(2)-x)+cot(2 pi+x)}=1

Prove that: (a) (cos(pi+x) cos(-x))/(sin(pi-x)cos(pi/2+x))=cot^(2)x (b) cos((3pi)/2 + x)cos(2pi+x){cot ((3pi)/2-x)+cot(2pi+x)}=1

Prove that: (cos(pi+x)cos(-x))/(sin(pi-x)cos(pi)/(2)+x)=cot^(2)x

Prove that: (cos(pi+x)cos(-x))/(sin(pi-x)cos((pi)/(2)+x))=cot^(2)x

Prove that: cos((3 pi)/(4)+x)-cos((3 pi)/(4)-x)=sqrt(2)sin x

Prove that: cos((3 pi)/(4)+x)-cos((3 pi)/(4)-x)=-sqrt(2)sin x

Prove that: cos((3 pi)/(4)+x)-cos((3 pi)/(4)-x)=-sqrt(2)sin x

Prove that cos x+cos((2 pi)/(3)-x)+cos((2 pi)/(3)+x)=0