" 5."log|cos^(-1)x|

f(x)=log_(5)(cos^(-1)sqrt(x^(2)+5x+6)+sec^(-1)[{x}+1]([.] denotes greatest integer function and {.} denotes fractional part function. Find the domain of f(x) :

f(x)=log_(5)(cos^(-1)sqrt(x^(2)+5x+6)+sec^(-1)[{x}+1]([.] denotes greatest integer function and {.} denotes fractional part function. Find the domain of f(x) :

The derivative of cos h ^(-1) x with respect to log x at x=5 is

int(sin2x)/(sin^(2)x+2cos^(2)x)dx(i)-log(1+sin^(2)x)+C(ii)log(1+cos^(2)x)+C( iii) -log(1+cos^(2)x)+C(iv)log(1+tan^(2)x)+C

int(sin2x)/(sin^(2)x+2cos^(2)x)dx(i)-log(1+sin^(2)x)+C(ii)log(1+cos^(2)x)+C( iii) -log(1+cos^(2)x)+C(iv)log(1+tan^(2)x)+C

The solution of the inequality "log"_(2) sin^(-1) x gt "log"_(1//2) cos^(-1) x is

The solution of the inequality "log"_(2) sin^(-1) x gt "log"_(1//2) cos^(-1) x is

int (dx)/(1 + tan x) is equal to a) (1)/(2) + (1)/(2)log|cos x + sin x|+C b) (x)/(2) + (1)/(2) log|cos x - sin x| +C c) (1)/(2) + (1)/(2) log|cos x - sin x| + C d) (x)/(2) + (1)/(2) log|cos x + sin x| + C

Number of solutions of the equation log_(10) ( sqrt(5 cos^(-1) x -1 )) + 1/2 log_(10) ( 2 cos^(-1) x + 3) + log_(10)sqrt5 = 1 is

Number of solutions of the equation log_(10) ( sqrt(5 cos^(-1) x -1 )) + 1/2 log_(10) ( 2 cos^(-1) x + 3) + log_(10)sqrt5 = 1 is