[" 8.(i) "1+(cot^(2)theta)/((1+cosec theta))=cosec theta],[" (ii) "1+tan^(2)theta" - "cos theta]

1+(cot^(2)theta)/(1+csc theta)=csc theta

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

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

show that 1 + (cot^2 theta/ (1 + cosec theta)) = cosec theta

Prove that : (i) 1+(cos^(2)theta)/(sin^(2)theta)-"cosec"^(2)theta=0 (ii) (1+tan^(2)theta)/("cosec"^(2)theta)=tan^(2)theta

Prove that : (i) 1+(cos^(2)theta)/(sin^(2)theta)-"cosec"^(2)theta=0 (ii) (1+tan^(2)theta)/("cosec"^(2)theta)=tan^(2)theta

(cot theta)/((cosec theta+1))+((cosec theta+1))/(cot theta)=2sec theta

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

(cos theta)/(cosec theta+1)+(cos theta)/(cosec theta-1)=2tan theta

Prove that: ("cosec" theta + cot theta)/("cosec" theta - cot theta) = ("cosec" theta + cot theta )^(2) = 1 + 2 cot^(2) theta + 2 "cosec" theta cot theta .