यदि` tan .(theta)/(2)= ((1+e)/(1-e))^(1//2) . tan .(phi)/(2)` तो सिध्द कीजिए कि:
`cos theta =.(cos phi)/(1-e cos phi) `

Explanation

बायाँ पक्ष : `cos theta = (1- tan^(2).(theta)/(2))/(1+ tan^(2) .(theta)/(2))= (1-(1+3)/(1-e)tan^(2).(phi)/(2))/(1+(1+e)/(1-e) tan^(2) .(phi)/(2))`
`=((1-e)-(1+e)tan^(2).(phi)/(2))/((1-e)+(1-e)tan^(2).(phi)/(2))`
` =((1- tan^(2).(phi)/(2))-e(1+tan^(2).(phi)/(2)))/((1+tan^(2).(phi)/(2))-e (1-tan^(2) .(phi)/(2)))`
अंश तथा हर को `1 + tan^(2) .(phi)/(2)` से भाग देने पर
`cos theta =((1-tan^(2).(phi)/(2))/(1+tan^(2).(phi)/(2))-e)/(1-e.(1-tan^(2).(phi)/(2))/(1+tan^(2).(phi)/(2)))=(cos phi -e)/(1-ecos phi) =`दायाँ पक्ष।