Prove each of the following identities : `(1+ tan^(2) theta)(1+ cot^(2) theta)=(1)/((sin^(2) theta- sin^(4) theta)) `

Prove each of the following identities : `(1+ tan^(2) theta)(1+ cot^(2

1.	Prove each of the following identities : `(1+ tan^(2) theta)(1+ cot^(2) theta)=(1)/((sin^(2) theta- sin^(4) theta)) `
Answer» LHS ` = sec^(2) theta * "cosec"^(2) theta = (1)/(cos^(2) theta sin^(2) theta ) ` ` = (1)/(sin^(2)theta (1-sin^(2) theta) ) = (1)/((sin^(2) theta - sin^(4) theta )) .`

`1/(c o s e ctheta-cottheta)-1/(sintheta)=1/(sintheta)-1/(c o s e ctheta+cottheta)`
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Prove that `(sin theta + "cosec" theta)^(2)+(cos theta + sec theta)^(2)=(7+ tan^(2) theta + cot^(2) theta).`
Prove that `(i) (1- sin theta)/(1+ sin theta)=(sec theta - tan theta )^(2) ` `(ii) ((1+cos theta))/((1- cos theta))= ("cosec" theta + cot theta)^(2)`