[" Prove! "],[qquad (tan theta-cot theta)/(sin theta cos theta)=sec^(2)theta-cosec^(2)theta]

Prove the following identity : (tan theta-cot theta)/ (sin theta cos theta)= sec^2 theta- cosec^2 theta .

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

(sin theta" cosec "theta tan theta cot theta)/(sin^(2)theta+cos^(2)theta)

" (2.) "tan theta+cot theta=sec theta cosec theta

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

(cosec theta+sin theta)(cosec theta-sin theta)=cot^(2)theta+cos^(2)theta

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

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

Prove that: ((1+ cot theta + tan theta)(sin theta - cos theta))/(sec^(3)theta - "cosec"^(3)theta) = sin^2 theta cos^2 theta

Prove that ((1+cot theta +tan theta)(sin theta - cos theta))/(sec ^3 theta -cosec^3 theta) = sin^2 theta cos^2 theta.