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If cos theta= (cos alpha-cos beta)/(1- c...

If `cos theta= (cos alpha-cos beta)/(1- cos alpha cos beta)`, then prove that one of the values of `tan. (theta)/(2) ` is `tan. (alpha)/(2) cot. (beta)/(2)`

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`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)`.
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