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

Show that cot(pi/4+x)cot(pi/4-x)=1

The value of the expression cos((pi)/(2)-x)cos((3 pi)/(2)+x)-cos(pi-x)cos(2 pi-x)

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

(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

(sin (pi + x) cos ((pi) / (2) + x) tan ((3 pi) / (2) -x) cot (2 pi-x)) / (sin (2 pi-x) cos (2 pi + x) csc (-x) sin ((3 pi) / (2) -x)) = 1