Prove that :
(i) `(1)/(1+tan^(2)theta)+(1)/(1+cot^(2)theta)=1`
(ii) `sin^(2)theta+(1)/(1+tan^(2)theta)=1`

Prove that : sin^(2)theta+(1)/(1+tan^(2)theta)=1

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

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

(1+(1)/(tan^(2)theta))(1+(1)/(cot^(2)theta))=(1)/(sin^(2)theta-sin^(4)theta)

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

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

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

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

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

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