`sin^-1 xgtcos^-1x` holds for` (A) all of value of x (B) `xepsilon (0, 1/sqrt(2))` (C) `xepsilon ( 1/sqrt(2), 1)` (D) `x=0.75`

int_(0)^(1//sqrt(2))(x sin^(-1)x)/(sqrt(1-x^(2)))dx=

d/(dx)(sin^(-1)x+cos^(-1)x) is equal to : (A) (1)/(sqrt(1-x^(2))), (B) (2)/(sqrt(1-x^(2))), (C) 0 (D) sqrt(1-x^(2))

lim_(x to 0) (x +2 sin x)/(sqrt(x^(2)+2 sin x + 1)-sqrt(sin^(2) x - x+ 1)) is

If cos (sin^(-1)(2/sqrt(5)) + cos^(-1)x) = 0, then x is equal to A) 1/sqrt(5) B) (-2/sqrt(5)) C) (2/sqrt(5)) D) 1

The trigonometric equation sin^(-1)x=2sin^(-1)a has a solution for all real values (b) |a|<(1)/(a)|a|<=(1)/(sqrt(2))( d) (1)/(2)<|a|<(1)/(sqrt(2))

A solution of sin^-1 (1) -sin^-1 (sqrt(3)/x^2)- pi/6 =0 is (A) x=-sqrt(2) (B) x=sqrt(2) (C) x=2 (D) x= 1/sqrt(2)

if x=(sqrt2 + 1 ) ^(-1//3) , then the value of (x^3 - frac(1) (x^3)) is (A) 0 (B) -sqrt2 (C ) -2 (D) 3sqrt2

The value of cos(2cos^-1x+sin^-1x) at x= 1/5 is (A) 1 (B) 3 (C) 0 (D) (-2sqrt(6))/5

Which of the following identities does not hold? (A) sin^-1 x = cot^-1[sqrt((1-x^2))/x],0ltxle1 (B) sin^-1 x = cot^-1[sqrt((1-x^2))/x],-1,=xlt0 (C) sin^-1 x = cos^-1 sqrt(1-x^2),0ltxle1 (D) sin^-1 x= 1-sin^-1 (-x), -1lexle1