If `cos theta=(cos alpha-cos beta)/(1-cos alpha cos beta),`prove that `tan theta/2=+-tan alpha/2 cot beta/2.`

Explanation

`tan^(2)""(theta)/(2)=(1-costheta)/(1+cos theta)`
`=(1-(cos alpha -cos beta)/(1-cos alpha cos beta))/(1+(cosalpha-cos beta)/(1-cos alpha cos beta))`
`=(1-cos alpha cos beta-cos alpha+cos beta)/(1-cos alpha cos beta+cos alpha-cos beta)`
`=((1-cos alpha)+cosbeta(1-cosalpha))/((1+cos alpha)-cos beta(1+cos alpha))`
`therefore tan ((theta)/(2))=+-tan ((alpha)/(2))cot((beta)/(2))`
Hence, one of the values of `tan"" (theta)/(2)` is `tan"" (alpha)/(2) cot"" (beta)/(2)`.