If `sinalpha+sinbeta=a\ and\ cosalpha-cosbeta=b ,` then `tan(alpha-beta)/2=` `-a/b` b. `-b/a` c. `sqrt(a^2+b^2)` d. none of these

Explanation

`sin C+sin D=2 sin frac{C+D}{2} cos frac{C-D}{2}`


`cos C-cos D=-2 sin frac{C+D}{2} sin frac{C-D}{2}`


`sin alpha+sin beta=2 sin frac{alpha+beta}{2} cos frac{alpha-beta}{2}=a`


`frac{cos alpha-cos beta}{-2 sin frac{alpha+beta}{2} sin frac{alpha-beta}{2}}=frac{b}{a}`


`2 sin frac{alpha+beta}{2} cos frac{alpha-beta}{2} sin frac{alpha-beta}{2}=b`


`=frac{sin }{sin frac{alpha-beta}{2}}=frac{-b}{a}`


`cos frac{alpha-beta}{2}`


`frac{a}{2}=frac{b}{a}`