" (a) "f_(48)" anfors for "1+((1-tan theta)/(1-cot theta))^(2)=sec^(2)theta

prove that 1+((1-tan theta)/(1-cot theta))^(2)=sec^(2)theta

1+(tan^(2)theta)/((1+sec theta))=sec theta

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

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

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

(1+tan^(2)theta)/(1+cot^(2)theta)=((1-tan theta)/(1-cot theta))^(2)

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

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

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

( tan^(3) theta )/( 1+ tan^(2) theta )+ ( cot^(3) theta )/( 1+ cot^(2) theta )=