If `sin^(-1)x+cot^(-1)(1/2)=pi/2,\ t h e n\ x` is `0` b. `1/(sqrt(5))` c. `2/(sqrt(5))` d. `(sqrt(3))/2`

If tan(cos^(-1)x)="sin"(cot^(-1)(1/2)) then x is equal to- a. 1/sqrt(5) b. 2/sqrt(5) c. 3/sqrt(5) d. sqrt(5)/3

If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x , is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3) (d) sqrt(2)

If 4\ cos^(-1)x+sin^(-1)x=pi , then the value of x is (a) 3/2 (b) 1/(sqrt(2)) (c) (sqrt(3))/2 (d) 2/(sqrt(3))

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

If |cos^(-1)((1-x^2)/(1+x^2))| < pi/3,t h e n (a) x in [-1/3,1/(sqrt(3))] (b) x in [-1/(sqrt(3)),1/(sqrt(3))] x in [0,1/(sqrt(3))] (d) none of these

If 3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-2)((2x)/(1-x^2))=pi/3, w h e r e|x|<1, then x is equal to 1/(sqrt(3)) (b) -1/(sqrt(3)) (c) sqrt(3) (d) -(sqrt(3))/4

If sin^(-1)x + tan ^(-1) x = (pi)/(2) , then prove that 2x^(2) + 1 = sqrt(5)

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

If sin^(-1)x+tan^(-1)x=(pi)/(2) , prove that : 2x^(2)+1=sqrt(5)

sin^(-1)(2xsqrt(1-x^2))=2sin^(-1)x is true if x in [0,\ 1]\ b. [-1/(sqrt(2)),1/(sqrt(2))] c. [-1/2,1/2] d. [-(sqrt(3))/2,(sqrt(3))/2]