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If for x in (0, (pi)/(2) ) , log (10) s...

If for `x in (0, (pi)/(2) ) , log _(10) sin x + log _(10) cos x =-1 and log _(10) (sin x + cos x) = (1)/(2) ( log _(10) n-1), n gt 0,` then the value of n is equal to :

A

1

B

12

C

`2 ^(n-1)`

D

n

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