सिद्ध करें कि
`= ( 1+ tan . ( theta)/( 2))/( 1- tan . (theta)/(2)) = ( 1+ sin theta)/( cos theta) = tan ((pi)/(4) + ( theta)/( 2))`

Explanation

बायाँ पक्ष `((1+ sin.(theta)/(2))/(cos.(theta)/(2)))/(sin.(theta)/(2))=(cos . (theta)/(2) +sin . (theta)/(2))/(cos . (theta)/(2) - sin. (theta)/(2))=((cos . (theta)/(2)+sin. (theta)/(2)))/(cos^(2).(theta)/(2)-sin^(2). (theta)/(2))`
`= (cos . (theta)/(2)+sin. (theta)/(2)+2 sin. (theta)/(2) cos. (theta)/(2))/(cos^(2). (theta)/(2) - sin^(2). (theta)/(2))=(1+sin theta)/(cos theta)`
पुनः `(1+ tan. ( theta)/(2))/(1-tan. (theta)/(2)) = ( tan. ( pi)/(4) + tan. ( theta)/(2))/( 1- tan. ( pi)/(2) tan. ( theta)/(2))= tan ((pi)/(4) + ( theta)/(2))`
इस प्रकार `( 1+ tan. ( theta)/(2))/(1- tan. (theta)/(2))= ( 1+ sin theta)/( cos theta) = tan. ((pi )/(4) + ( theta)/(2))`