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

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

1.	Prove each of the following identities : `(1+ tan theta + cot theta )( sin theta - cos theta ) =((sec theta)/("cosec"^(2) theta ) - ("cosec"theta)/(sec^(2)theta)) `
Answer» `LHS=(1+(sintheta)/(costheta)+(costheta)/(sintheta))(sintheta -costheta)=((sinthetacostheta+sin^(2)theta+cos^(2)theta)(sintheta-costheta))/(sinthetacostheta)` `=((sin^(3)theta -cos^(3)theta))/(sinthetacostheta)=((sin^(3)theta)/(sinthetacostheta)-(cos^(3)theta)/(sinthetacostheta))=((sin^(2)theta)/(costheta)-(cos^(2)theta)/(sintheta))` `=((sectheta)/("cosec"^(2)theta)-("cosec"^(2)theta)/(sec^(2)theta))=RHS.`

`1/(c o s e ctheta-cottheta)-1/(sintheta)=1/(sintheta)-1/(c o s e ctheta+cottheta)`
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