सिद्ध कीजिए कि ` (sin (A -C)+2 sin A+ sin(A+C))/(sin (B-C)+2 sin B+sin (B+C))=(sinA)/(sinB)`

Explanation

` L.H.S = (sin (A-C)+2sinA+sin(A+C))/(sin(B-C)+2 sinB+sin(B+C))`
` = (sin (A+C) +sin (A-C) +2sin A )/(sin(B+C)+sin(B-C)+2 sinB)`
` 2 sin. (A+C+A-C)/2 `
` (*cos. ((A+C-A+C))/2 + sinA)/(2sin. (B+C+B-C)/2)`
` * cos. (B+C-B+C)/2 + 2 sin B`
` = ( 2 sin A cos C + 2 sin A )/(2 sin B cos C + 2 sin B)`
` = (sin A (2 cos C+2))/(sin B (2 cos C +2))= (sinA)/(sinB) = R.H.S`