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

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

If sin^(-1) x + sin^(-1) y = pi/2 , prove that x sqrt(1-y^2) + y sqrt(1-x^2) =1 .

If tan^(-1).(a+x)/(a) + tan ^(-1) ((a-x)/(a)) = (pi)/(6) then prove that x^(2) = 2sqrt(3)a^(2)

If x=sin(2tan^(-1)2)and y=sin((1)/(2)tan^(-1).(4)/(3)) , then prove that y^2 = 1 - x

Prove that : cos^(-1) x = 2 cos^(-1) sqrt((1+x)/(2)) (ii) Prove that : tan^(-1)((cosx + sin x)/(cosx - sin x)) = (pi)/(4)+ x

Number of values of x satisfying simultaneously sin^(-1) x = 2 tan^(-1) x " and " tan^(-1) sqrt(x(x-1)) + cosec^(-1) sqrt(1 + x - x^(2)) = pi/2 , is

If tan (cot x) = cot (tan x) , prove that : sin 2x = 4/((2n+1) pi)

If cos^(-1)x+2sin^(-1)x+3cot^(-1)y+4tan^(-1)y=4sec^(-1)z+5cosec^(-1)z , then prove that sqrt(z^2-1)=(sqrt(1+x^2)-xy)/(x+ysqrt(1-x^2))

Prove that sin^(-1). ((x + sqrt(1 - x^(2))/(sqrt2)) = sin^(-1) x + (pi)/(4) , where - (1)/(sqrt2) lt x lt(1)/(sqrt2)

If tan(sin^(-1)sqrt(1-x^2))=sin(tan^(-1)2) then x is