Prove that : `sin^(-1)x+cos^(-1)x=(pi)/(2), |x| le 1`

Prove that sin^(-1) cos (sin^(-1) x) + cos^(-1) x) = (pi)/(2), |x| le 1

Prove that sin^(-1)x=cos^(-1) sqrt(1-x^2)

prove that sin^(-1)(x)+cos^(-1)(x)=pi/2 , -1<=x<=1

If |sin^(-1)x|+|cos^(-1)x|=(pi)/(2), then x in

If |sin^(-1)x|+|cos^(-1)x|=(pi)/(2), then x in

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 :

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 :

Prove that : 2sin^(-1). ((2x )/(1+x^(2))), -1 le x lt 1

Prove that : sin^(-1) (2x sqrt(1-x^(2)) ) = 2 sin^(-1) x , -1/(sqrt(2))le x le 1/(sqrt(2)