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The number of ordered pairs (α,β), where...

The number of ordered pairs (α,β), where α,β∈(−π,π) satisfying cos (α−β)=1 and cos(α+β)=1/e is

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`cos(alpha-beta)=1`
`cos(alpha-beta)=cos0`
`alpha-beta=0`
`alpha=beta`
`cos(alpha+beta)=1/e`
`cos2alpha=1/e`
`alpha=beta=4`
Option D is correct.
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