Which of the folllowing functions are defined for all x (A) `sin[x]+ cos[x}([x]}`denotes the greatest integers` le x`)(B) `sec^(-1) (1 + sin^2 x) `(C)` tan(logx)` (D) `sqrt(9/8+cos x+cos 2x)`

Period of f(x) = sin 3x cos[3x]-cos 3x sin [3x] (where[] denotes the greatest integer function), is

The number of solutions of [sin x+ cos x]=3+ [- sin x]+[-cos x] (where [.] denotes the greatest integer function), x in [0, 2pi] , is

Which of the following functions is not periodie? (a) |sin3x|+sin^2x (b) cossqrt(x)+cos^2x (c) cos4x+tan^2x (d) cos2x+sinx

Domain (D) and range (R) of f(x)=sin^(-1)(cos^(-1)[x]), where [.] denotes the greatest integer function, is

lim_(xrarr0) [(sin^(-1)x)/(tan^(-1)x)]= (where [.] denotes the greatest integer function)

int (sin^(8) x - cos ^(8) x)/( 1 - 2 sin^(2) x cos^(2) x) dx is

sin (n +1) x sin (n +2) x + cos (n +1) x cos (n +2) x = cos x

Prove that sin^(6)x + cos^(6)x = 1 - 3 sin^(2) x cos^(2)x .

Find the values of x for which the following pair of functions are identical. (i) f(x)=tan^(-1)x+cot^(-1)x " and " g(x)=sin^(-1)x +cos^(-1)x (ii) f(x)=cos(cos^(-1)x) " and " g(x)=cos^(-1)(cosx)

Differentiate the functions w.r.t. x. (x cos x)^(x)+ ( x sin x)^(1/x) .