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If "log"(10) sin x+"log"(10)cos x=-1 and...

If `"log"_(10) sin x+"log"_(10)cos x=-1 and "log"_(10)(sin x+cosx)=(("log"_(10)n)n-1)/(2)` then the value of n is ____________

A

9

B

20

C

12

D

16

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