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

Trigonometric Ratio and Identites

JEE Main 2021 · 16 Mar, Morning shift · Q5646

MathematicsMedium45×since 2004Q5646

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 :

JEE Main 2021 · 16 Mar, Morning shift · Q5646

MathematicsMedium45×since 2004Q5646

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 :