सिद्ध कीजिए कि
` (sin theta)/(1+ cos theta ) + (1+ cos theta )/(sin theta )= 2 "cosec" theta `

Explanation

` L.H.S = (sintheta)/(1+costheta)+ (1= costheta)/(sintheta)`
`= (sin^(2) theta + ( 1+ cos theta)^(2))/((1+ cos theta) * sin theta)`
` = ( sin^(2) theta+ 1 + cos^(2) theta + 2 cos theta)/((1+cos theta ) * sin theta)`
` = (( sin^(2) theta + cos^(2) theta) + 1 + 2 cos theta )/((1+ cos theta) * sin theta)`
` = ( 1+ 1+ 2 cos theta )/( (1+cos theta) * sin theta) = ( 2 (1+cos theta))/((1+costheta)sin theta)`
` = 2/(sin theta) = 2 "cosec" theta = R.H.S`