sec theta[1-sin theta)cosec theta+tan theta2=1

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

Prove the following identity : (sec theta-cos theta) (cosec theta-sin theta)=1/(tan theta+ cot theta) .

(1/(cos theta)-1/(sin theta))+1/(cosec theta-cot theta)-1/(sec theta+tan theta) =?

(cosec theta -sin theta ) (sec theta - cos theta ) (tan theta + cot theta ) = 1.

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

Prove that (i) (1- sin theta)/(1+ sin theta)=(sec theta - tan theta )^(2) (ii) ((1+cos theta))/((1- cos theta))= ("cosec" theta + cot theta)^(2)

Prove that: ((1)/(cos theta)-(1)/(sin theta))(1+(sin theta)/(cos theta)+(cos theta)/(sin theta))=sec theta tan theta-cosec theta cot theta

Prove that (i) (1)/(("cosec" theta- cot theta ))=("cosec" theta + cot theta) (ii) ((sec theta - tan theta))/((sec theta + tan theta))=(1+ 2tan^(2) theta - 2 sec theta tan theta)

Prove that (i) (sin theta)/((1- cos theta))=("cosec" theta + cot theta) (ii) (1)/((sec theta - tan theta))=(sec theta + tan theta)

Prove that (i) (sin theta)/((1- cos theta))=("cosec" theta + cot theta) (ii) (1)/((sec theta - tan theta))=(sec theta + tan theta)