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If 3tanA tanB=1, then prove that 2cos(A+...

If `3tanA tanB=1`, then prove that `2cos(A+B)=cos(A-B)`

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We have,
`3tanAtanB=1`
`rArr (3sinAsinB)/(cosAcosB)=1`
`rArr (cosAcosB)/(sinAsinB)=3/1`
`rArr (cosAcosB+sinAsinB)/(cosAcosB-sinAsinB)=(3+1)/(3-1)` [Using componendo-dividendo]
`rArr (cos(A-B))/(cos(A+B))=2`
`rArr 2cos(A+B)=cos(A-B)`
Hence proved.
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