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If alpha and beta are acute angles such ...

If `alpha` and `beta` are acute angles such that `alpha+beta=lamda`, where constant, find the maximum possible value of the expression `sin alpha+sin beta+cos alpha+cos beta`.

Text Solution

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`sin alpha+sin beta+cos alpha+cos beta`
`=2sin((alpha+beta)/(2))cos((alpha-beta)/(2))+2cos((alpha+beta)/(2))cos((alpha-beta)/(2))`
`=2cos((alpha-beta)/(2))[sin""(lamda)/(2)+cos""(lamda)/(2)]le2[sin""(lamda)/(2)+cos""(lamda)/(2)]`
`=2sqrt(2)sin((lamda)/(2)+(pi)/(4))`
This is the maximum value of expression.
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