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If sinalpha-sinbeta=1/3andcosbeta-cosalp...

If `sinalpha-sinbeta=1/3andcosbeta-cosalpha=1/2,`show that `cot(alpha+beta)/2=2/3`

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`sin alpha-sinbeta=(1)/(3)`
`rArr 2sin((alpha-beta)/(2))cos((alpha+beta)/(2))=(1)/(3)`
`cos beta-cos alpha=(1)/(2)`
`rArr2sin((alpha-beta)/(2))sin((alpha+beta)/(2))=(1)/(2)`
Dividing Eqs. (i) by (ii), we have `cot""(alpha+beta)/(2)=(2)/(3)`.
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