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If cos A+cosB=1/2 and sin A+ sinB=1/4 ,...

If `cos A+cosB=1/2` and `sin A+ sinB=1/4` , prove that: `tan((A+B)/2)=1/2`

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Given,--
`=>cos A+cosB=1/2`
`=>2cos((A+B)/2)cos((A-B)/2)=1/2-------(i)`
Similaly,
`=>sinA+sinB=1/4`
`=>2sin((A+B)/2)cos ((A-B)/2)=1/4-------(ii)`
...
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