If `alpha,beta,gammain[0,pi] and alpha,beta,gamma` are in AP, then `(sinalpha-singamma)/(cosgamma-cosalpha)` is equal to

Options

A. `sin beta`
B. `cos beta`
C. `cot beta`
D. `cosec beta`

Answer

C

Explanation

Since, `alpha, beta and gamma` are in AP.
`therefore 2beta=alpha+gamma`
Now, `(sinalpha-singamma)/(cosgamma-cosalpha)=(2cos((alpha+gamma)/(2))sin((alpha-gamma)/(2)))/(2sin((alpha+gamma)/(2))sin((alpha-gamma)/(2)))`
`=cot((alpha+gamma)/(2))=cot((2beta)/(2))" "[because 2beta=alpha+gamma]`
`=cotbeta`