[" (i) "cot^(2)theta-(1)/(sin^(2)theta)=-1],[" (ii) "quad (1+tan^(2)theta)(1+sin theta)(1-sin theta)=1]

Prove the following trigonometric identities: cot^(2)theta-(1)/(sin^(2)theta)=-1 (ii) (1+tan^(2)theta)(1+sin theta)(1-sin theta)=1

Prove the following trigonometric identities: cos^(2)theta+(1)/(1+cot^(2)theta)=1 (ii) (1)/(1+sin theta)+(1)/(1-sin theta)=2sec^(2)theta

(sin^(2) theta)/(1-cos theta)-(cos^(2) theta)/(1-sin theta)=cos theta-sin theta

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

(cos theta)/(1 - tan theta) + (sin theta)/(1 - cot theta) =……...

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

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

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

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