Question

किसी त्रिभुज ABC में सिद्ध कीजिए कि - (i) `((cos^2A//2)/(a))+((cos^2B//2)/(b))+((cos^2C//2)/(c))=(s^2)/(abc)`
(ii) `tan.(A)/(2)tan.(B)/(2)tan.(C)/(2)=sqrt((1-(a)/(s))(1-(b)/(s))(1-(c)/(s)))`

Answer 1

बायाँ पक्ष `=(1)/(a)cos^2.(A)/(2)+(1)/(b)cos^2.(B)/(2)+(1)/(c)cos^2.(C)/(2)=(1)/(a)xx(s(s-a))/(bc)+(1)/(b)(s(s-b))/(ca)+(1)/(c)xx(s(s-c))/(ab)`
`=(1)/(abc)(s^2-sa+s^2-ab+s^2-sc)=(1)/(abc)[3s^2-s(a+b+c)]`
`=(1)/(abc)[3s^2-sxx2s]=(s^2)/(abc)=` दायाँ पक्ष