If `|sin^(-1)x|x|cos^(-1)x|=pi/2,t h e nx in ` `R` (b) `[-1,1]` (c) `[0,1]` (d) `varphi`

If |sin^(-1)x|+|cos^(-1)x|=(pi)/(2), then (a) x in R (b) [-1,1](c)[0,1](d)varphi

If sin^(-1)x-cos^(-1)x=pi/6 , then x= 1/2 (b) (sqrt(3))/2 (c) -1/2 (d) none of these

If y = sin^(-1) x then x belongs to the interval: (a) (0,pi) (b) (-1,1) (c) [-1,1] (d) [0,pi]

sin^(-1)x+cos^(-1)x,x in[-1,1]= (A) 0 (B) (pi)/(2) (C) pi (D) 2 pi

sin^(-1)x+cos^(-1)x,x in[-1,1]= (A) 0 (B) (pi)/(2) (C) pi (D) 2

sin^(-1)x+cos^(-1)x,x in[-1,1] = (A) 0 (B) pi/2 (C) pi (D) 2pi

It is given that A=(tan^(-1)x)^(3)+(cot^(-1)x)^(3) where x gt 0 and B=(cos^(-1)t)^(2)+(sin^(-1)t)^(2) where t in [0, (1)/(sqrt(2))] , and sin^(-1)x+cos^(-1)x=(pi)/(2) for -1 le x le 1 and tan^(-1)x +cot^(-1)x=(pi)/(2) for x in R . The maximum value of B is :

It is given that A=(tan^(-1)x)^(3)+(cot^(-1)x)^(3) where x gt 0 and B=(cos^(-1)t)^(2)+(sin^(-1)t)^(2) where t in [0, (1)/(sqrt(2))] , and sin^(-1)x+cos^(-1)x=(pi)/(2) for -1 le x le 1 and tan^(-1)x +cot^(-1)x=(pi)/(2) for x in R . The interval in which A lies is :

If a sin^(-1)x-b cos^(-1)x=c, then a sin^(-1)x+b cos^(-1)x is equal to (a)0(b)(pi ab+c(b-a))/(a+b)(c)(pi)/(2)(d)(pi ab+c(a-b))/(a+b)

If tan^(-1)(a+x)/a+tan^(-1)(a-x)/a=pi/6,t h e nx^2= 2sqrt(3)a (b) sqrt(3)a (c) 2sqrt(3)a^2 (d) none of these