सिद्ध कीजिए कि `(cos(90^(@)+theta)sec(270^(@)+theta)sin(180^(@)+theta))/("cosec "(-theta)cos(270^(@)-theta)tan(180^(@)+theta))=cos theta`

Explanation

बायाँ पक्ष `=(cos(90^(@)+theta)sec(270^(@)+theta)sin(180^(@)+theta))/("cosec "(-theta)cos(270^(@)-theta)tan(180^(@)+theta))=cos theta`
`=(cos(90^(@)+theta)sec{180^(@)+(90^(@)+theta)}sin(180^(@)+theta))/(-"cosec "theta cos {180^(@)+(90^(@)-theta)}tan(180^(@)+theta))`
`=(cos(90^(@)+theta){-sec(90^(@)+theta)}-{-sin theta})/(-"cosec "theta{-cos(90^(@)-theta)}tan theta)`
`" "sin (180^(@)+theta )=-sin theta`
`" " cos(180^(@)+theta)=-cos theta`
`tan(180^(@)+theta)=tan theta`
`" व "sec(180^(@)+theta)=-sec theta" का प्रयोग करते हुए")`
`=((-sin theta)"cosec "theta(-sin theta))/((-"cosec "theta)(-sin theta)tan theta)" "cos (90^(@)+theta)=-sin theta`
`" "sec(90^(@)+theta)= -"cosec "theta`
`" "cos(90^(@)-theta)=sin theta` का प्रयोग करते हुए
`=cos theta = ` दायाँ पक्ष