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If cos x-sinx=-(5)/(4), where (pi)/(2)lt...

If `cos x-sinx=-(5)/(4)`, where `(pi)/(2)ltx lt(3pi)/(4)`, then `cot((x)/(2))` is equal to

A

`(4-sqrt7)/(9)`

B

8

C

`-8`

D

`(4+sqrt7)/(9)`

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The correct Answer is:
D
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