If for \( \mathrm{x} \in\left(0, \frac{\pi}{2}\right), \log _{10} \...

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If for \( \mathrm{x} \in\left(0, \frac{\pi}{2}\right), \log _{10} \sin \mathrm{x}+\log _{10} \cos \mathrm{x}=-1 \) and \( \log _{10}(\sin \)
\( \mathrm{P} \) \( x+\cos x)=\frac{1}{2}\left(\log _{10} n-1\right), n0 \) then the value of \( n \) is equal to:
(a) 20
[JEE Main-2021 (March)]
(b) 12
(c) 9
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