If `sin^(- 1)(x-(x^2)/2+(x^3)/4-.....)+cos^(- 1)(x^2-(x^4)/2+(x^6)/4-.....)=pi/2` for `0 lt |x| lt sqrt2` then `x=`

If cot^(-1)(x-(x^(2))/(2)+(x^(3))/(4)-…………..)+tan^(-1)(x^(2)-(x^(4))/(2)+(x^(6))/(4)-……..)=(pi)/(2)" for "0lt |x| lt sqrt2 , then x is equal to

The number of values of x for which sin^(-1)(x^2-(x^4)/3+(x^6)/9)+cos^(-1)(x^4-(x^8)/3+(x^(12))/9ddot)=pi/2, where 0lt=|x|

Prove that sin^(-1) {(sqrt(1 + x) + sqrt(1 - x))/(2)} = (pi)/(4) + (cos^(-1) x)/(2), 0 lt x lt 1

If |x|lt1 and y=x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+... , then x =

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

If sec x cos 5x+1=0 , where 0lt x lt 2pi , then x=

Solve (x^2-4)sqrt(x^2 -1) lt 0.

Prove that cos^(-1) {sqrt((1 + x)/(2))} = (cos^(-1) x)/(2) , -1 lt x lt 1

3(1 - x ) lt 2 (x + 4)

Solve sin^(-1) [sin((2x^(2) + 4)/(1 + x^(2)))] lt pi -3