prove that:
`(1-tan theta)^2+(1-cot theta)^2=(sec theta - cosec theta)^2`

prove that: (tan theta-cot theta)^(2)+2=sec^(2) theta+ cosec^(2) theta-2

prove that: tan^(2) theta-cot^(2) theta=sec^(2) theta- cosec^(2) theta

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

prove that: (tan theta)/(1-cot theta)+(cot theta)/(1-tan theta)=1+sec theta cosec theta

prove that tan theta/(sec theta+1)+cot theta/(cosec theta+1)=cosec theta+sec theta-cosec theta. sec theta

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