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If costheta=(cosalpha-cosbeta)/(1-sinalp...

If `costheta=(cosalpha-cosbeta)/(1-sinalphasinbeta)` , prove that one value of `t a ntheta/2=(t a nalpha/2-t a nbeta/2)/(1-t a nalpha/2-t a nbeta/2)`

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`cos theta=frac{cos alpha-cos beta}{1-cos alpha cos beta}`

or, `frac{1-tan ^{2} frac{theta}{2}}{1+tan ^{2} frac{theta}{2}}=frac{cos alpha-cos beta}{1-cos alpha cos beta}`

or, `frac{1+tan ^{2} frac{theta}{2}}{1-tan ^{2} frac{theta}{2}}=frac{1-cos alpha cos beta}{cos alpha-cos beta}`
or `t a ntheta/2=(t a nalpha/2-t a nbeta/2)/(1-t a nalpha/2-t a nbeta/2)` or, `tan ^{2} frac{theta}{2}=frac{1-cos alpha cos beta-cos alpha+cos beta}{1-cos alpha cos beta+cos alpha-cos beta}`

or, `tan ^{2} frac{theta}{2}=frac{(1-cos alpha)(1+cos beta)}{(1+cos alpha)(1-cos beta)}`

or, `tan^2 frac{theta}{2}=tan 2 frac{alpha}{2} cos ^2 frac{beta}{2}`

or, `tan ^{2} frac{theta}{2}=pm tan frac{alpha}{2} cot frac{beta}{2}`
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