Prove that `(costheta \ cos(90^@-theta))/(cot(90^(@)-theta))=cos^2theta`

Prove that (cos theta cos(90^(@)-theta))/(cot(90^(@)-theta))=cos^(2)theta

Prove that : (i) sinthetacos(90^(@)-theta)+sin(90^(@)-theta)costheta=1 (ii) sectheta" cosec"(90^(@)-theta)-tanthetacot(90^(@)-theta)=1 (iii) (sintheta*sec(90^(@)-theta)cot(90^(@)-theta))/("cosec"(90^(@)-theta)*costheta*tantheta)-(tan(90^(@)-theta))/(cottheta)=0 (iv) (1+sin(90^(@)-theta))/(cos(90^(@)-0))+(cos(90^(@)-theta))/(1+sin(90^(@)-0))=2"cosec"theta

Prove that : (i) sinthetacos(90^(@)-theta)+sin(90^(@)-theta)costheta=1 (ii) sectheta" cosec"(90^(@)-theta)-tanthetacot(90^(@)-theta)=1 (iii) (sintheta*sec(90^(@)-theta)cot(90^(@)-theta))/("cosec"(90^(@)-theta)*costheta*tantheta)-(tan(90^(@)-theta))/(cottheta)=0 (iv) (1+sin(90^(@)-theta))/(cos(90^(@)-0))+(cos(90^(@)-theta))/(1+sin(90^(@)-0))=2"cosec"theta

Prove that : (sin \theta . sin(90^(@) - \theta))/(cot (90^(@) - \theta)) = 1 - sin^(2) \theta

Prove that : (sinthetacos(90^0-theta)costheta)/(sin(90^0-theta))+(costhetasin(90^0-theta)sintheta)/(cos(90^0-theta))=1

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

Prove that (cos(90^(@)-theta))/(1+sin(90^(@)-theta))+(1+sin(90^(@)-theta))/(cos(90^(@)-theta))=2cosec theta

Prove that: (cos ec(90^(@)+theta)+cot(450^(@)+theta))/(cos ec(90^(@)-theta)+tan(180^(@)-theta))+(tan(180^(@)+theta)+sec(180^(@)-theta))/(tan(360^(@)+theta)-sec(-theta))=2

sin theta cos(90^(@)-theta)+cos theta sin(90^(@)-theta)

Prove that :(sin theta cos(90^(0)-theta)cos theta)/(sin(90^(0)-theta))+(cos theta sin(90^(0)-theta)sin theta)/(cos(90^(@)-theta))=1csc^(2)(90^(@)-theta)-tan^(2)theta=cos^(2)(90^(@)-theta)+cos^(2)theta