If log_(10) sin x+log_(10)cos x=-1 and log_(10)(sinx+cosx)=(log_(10)n-1)/2 then the value of n is (a) 24 (b) 36 (c) 20 (d) 12_

Answer

12

Explanation

Given `log_(10)((sin2x )/( 2))= -1 `
or `( sin 2x )/(2)= (1)/(10)`
or `sin 2x = (1)/(5)" " `…(i)
Also `log_(10) ( sin x + cos x ) = ( log_(10)((n)/(10)))/(2)`
or `log_(10)(sin x + cosx )^(2) = log_(10) ((n)/(10))`
or `1 + sin 2x = (n)/(10)`
or `1 + (1)/(5) = (n)/(10)`
or `(6)/(5) = (n)/(10)`
`therefore n = 12`