सिद्ध कीजिए कि `(cosec theta - sin theta) (sec theta - cos theta) (sec theta - cos theta) = 1/(tan theta + cot theta) `

Explanation

L.H.S. ` = (cosec theta - sin theta) ( sec theta - cos theta)`
` = (1/(sin theta) - sin theta)(1/(cos theta) - cos theta )" "[(.:' cosec theta = 1/(sin theta)),(sec theta = 1/(cos theta ))]`
` = ((1 - sin^(2) theta)/(sin theta)) ((1-cos^(2) theta)/(cos theta)) = (cos^(2) theta)/(sin theta) xx (sin^(2) theta)/(cos theta) = sin theta * cos theta ` ....(i)
`R.H.S. = 1/(tan theta + cot theta) = 1/((sin theta )/(cos theta) + (cos theta)/(sin theta)) = 1/((sin^(2) theta + cos^(2) theta)/(cos theta sin theta))" "[(.:'tan theta = (sin theta)/(cos theta)),(cot theta = (cos theta)/(sin theta))]`
` = 1 xx (cos theta sin theta )/1 = sin theta cos theta [:' sin^(2) theta + cos^(2) theta = 1]` .....(ii)
` :. ` (i) और (ii) से , L.H.S. = R.H.S.