Prove:
`(1 + cot^2 theta) (1 + cos theta)(1-cos theta)` = 1

Prove: 1+(cot^(2)theta)/(1+cos ec theta)=cos ec theta

Prove that (1+cos theta)/(1-cos theta)+(1-cos theta)/(1+cos theta)=4cot theta*cos theta

Prove: cos^2 theta + 1/(1 + cot^2 theta) = 1

Prove: 1+(cot^2theta)/(1+cos e c\ theta)=cos e c\ theta

Prove that ( cot theta - cosec theta)^(2) = ( 1- cos theta )/( 1+ cos theta )

Prove each of the following identities : (i) (1+ cos theta)(1- cos theta)(1+ cot^(2) theta)=1 (ii) "cosec" theta (1+ cos theta)("cosec" theta - cot theta)=1

Prove the following trigonometric identities : (1+cot^(2)theta)(1-cos theta)(1+cos theta)=1( ii) tan^(2)theta-(1)/(cos^(2)theta)=-1

Prove (cos ec theta-cot theta)^(2)=(1-cos theta)/(1+cos theta)

Prove: (1+cos theta-sin^(2)theta)/(sin theta(1+cos theta))=cot theta

Prove that ((1+cos theta)/(1-cos theta))=("cosec"theta + "cot"theta)^(2)