Question

किसी `Delta ABC` में सिद्ध कीजिए कि -
(i) `2(b cos^2(C)/(2)+c cos^2(B)/(2))=a+b+c`
(ii) `2(a sin^2(C)/(2)+c sin^2(A)/(2))=a+c-b`
(iii) `(sinA+sinB)gt sinC`

Answer 1

(i)बायाँ पक्ष `=2(b cos^2.(C)/(2)+c cos^2.(B)/(2))=b.2cos^2.(C)/(2)+C.2cos^2.(B)/(2)`
`=b(1+cosC)+c(1+cosB)`
`=b+c+(bcos C+c cos B)=a+b+c`