" If "cosec(pi/2+theta)+x cos theta cot(pi/2-theta)=sin(pi/2+theta)," then "x=

Prove that (cos(pi +theta)cos (-theta))/(cos(pi-theta) cos (pi/2+theta))=-cot theta

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

Prove that: (cos(2 pi+theta)csc(2 pi+theta)tan(pi/2+theta))/(sec(pi/2+theta)cos theta cot(pi+theta))=1

sin(pi+theta)sin(pi-theta)cosec^2theta=

Prove that (cos(pi+theta)cos(-theta))/(cos(pi-theta)cos((pi)/(2)+theta))=-cot theta

sin""((pi)/2+ theta ) * cos (pi- theta ) * cot ""((3pi)/(2)+ theta ) - sin""((pi)/2- theta ) * sin""((3pi)/2 - theta ) * cot ""((pi)/2 + theta ) =

(cosec(2pi+theta)cos(2pi+theta)tan(pi/2+theta))/(sec(pi/2+theta)costhetacot(pi+theta))

Prove that cosec(pi/4+theta/2)cosec(pi/4-theta/2)=2sec theta