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

Explanation

LHS ` = (tan theta )/(sec^(4) theta ) + (cot theta )/("cosec"^(4) theta ) = ((sin theta)/(cos theta) xx cos^(4) theta ) + ((cos theta)/(sin theta) xx sin^(4) theta) `
` = (sin theta cos^(3) theta + sin^(3) theta cos theta ) = sin theta cos theta ( cos^(2) theta + sin^(2) theta ) = sin theta cos theta . `