सिद्ध कीजिए कि `cos((3pi)/(2)+theta)cos(2pi+theta)[cot((3pi)/(2)-theta)+cot(2pi+theta)]=1`

Explanation

बायाँ पक्ष `=cos((3pi)/(2)+theta)cos(2pi+theta)[cot((3pi)/(2)-theta)+cot(2pi+theta)]`
`=cos[pi+((pi)/(2)+theta)]cos (2pi+theta)[cot{pi+((pi)/(2)-theta)}+(2pi+theta)]`
`=-cos((pi)/(2)+theta)cos theta [cot((pi)/(2)-theta)+cot theta]`
`" "{:("["because" "cos(pi+theta)=-cos theta),(" "cot(pi+theta)=cot theta),(" और "cot(2pi+theta)=cot theta"]"),([because" "cos((pi)/(2)+theta)=-sin theta]):}`
`=sin theta cos theta [tan theta+cot theta]`
`=sin theta cos [(sin theta)/(cos theta)+(cos theta)/(sin theta)]`
`=sin theta cos theta ((sin^(2)theta+cos^(2)theta)/(sin theta cos theta))=1=` और दायाँ पक्ष