Prove that ` (cos theta)/((1-tan theta))+(sin theta)/((1-cot theta))=(cos theta+sin theta). `

Prove that ` (cos theta)/((1-tan theta))+(sin theta)/((1-cot theta))=(

1.	Prove that ` (cos theta)/((1-tan theta))+(sin theta)/((1-cot theta))=(cos theta+sin theta). `
Answer» We have ` "LHS " =(cos theta)/((1- tan theta))+(sin theta)/((1-cot theta))=(cos theta)/((1-(sin theta)/(cos theta)))+(sin theta)/((1- (cos theta)/(sin theta)))` ` =(cos ^(2)theta)/((cos theta- sin theta))+(sin^(2) theta)/((sin theta - cos theta))` ` =(cos^(2) theta)/(cos theta - sin theta)-(sin^(2) theta)/(cos theta - sin theta)` `=(cos^(2)theta - sin^(2)theta)/((cos theta - sin theta))=((cos theta- sin theta)(cos theta +sin theta))/((cos theta- sin theta)) ` ` =(cos theta+sin theta)= " RHS. " ` ` therefore "LHS " = " RHS." `

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