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If 0 lt alpha lt (pi)/(2), (pi)/(2) lt b...

If `0 lt alpha lt (pi)/(2), (pi)/(2) lt beta lt pi and cos alpha =(4)/(5), cos beta=-(3)/(5)`, find the value of `"cos"(alpha-beta)/(2)`. Show also that `beta=(pi)/(2)+alpha`.

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The correct Answer is:
`(1)/(sqrt(2))`
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