If for x $\in$ $\left( {0,{\pi \over 2}} \right)$, log10sinx + log10cosx = $-$1 and log10(sinx + cosx) = ${1 \over 2}$(log10 n $-$ 1), n > 0, then the value of n is equal to :

Question

If for x $\in$ $\left( {0,{\pi \over 2}} \right)$, log₁₀sinx + log₁₀cosx = $-$1 and log₁₀(sinx + cosx) = ${1 \over 2}$(log₁₀ n $-$ 1), n > 0, then the value of n is equal to :

Solution

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