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If 3t a n At a n B=1, prove that 2cos(A+...

If `3t a n At a n B=1,` prove that `2cos(A+B)=cos(A-B)dot`

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Given,
`=>3tanAtanB=1`
`=>(3sinAsinB​)/(cosAcosB)=1`
`=>(3sinAsinB​)/(cosAcosB)=1/3`
`=>(cosAcosB​)/(sinAsinB)=3`
using componendo and dividendo we have
`=>(cosAcosB+sinAsinB)/(cosAcosB−sinAsinB​)=(3+1)/(3-1)`
...
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