If for x (0,(π)/2), log₁₀sinx + log₁₀cosx = - 1 and log₁₀(sinx + cosx) = 1/2 (log₁₀ n - 1), n > 0, then the value of n is equal to:

Trigonometry: JEE Main 2021 Mathematics question

JEE Main 2021 · 16 Mar, Morning shift · Q5646

JEE Main 202116 Mar, Morning shiftMathematicsMediumTrigonometry118× since 2002

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 :