[(x-(x^(3))/(2)+(x^(3))/(4)-1)+cos(x^(3)-(x^(2))/(2)+(x^(4))/(4)-x)=(pi)/(2)cos theta],[1/2],[1],[-1/2]

For 0le|x|lesqrt(2) , if cos^(-1)(x^(2)-(x^(4))/(2)+(x^(6))/(4)-…)+sin^(-1)(x-(x^(2))/(2)+(x^(3))/(4))-…)=(pi)/(2) , then x=

sin^(-1)(x-(x^(2))/(2)+(x^(3))/(4)-...)+cos^(-1)(x^(2)-(x^(4))/(2)+(x^(6))/(4)-...*)=(pi)/(2) for 0<|x|

If sin^(-1)(x-(x^(2))/2+(x^(3))/4-……oo) +cos^(-1)(x^(2)-(x^(4))/2+(x^(6))/4-……..oo)=(pi)/2 and 0ltxltsqrt(2) then x=

If sin^(-1)(x-(x^2)/(2)+(x^3)/(4)-...infty)+cos^(-1)(x^2-(x^4)/(2)+(x^6)/(4)-...infty)=(pi)/(2) and 0ltxltsqrt(2) , then x is equal to

Prove that cos^(-1)(x)+ cos^(-1){(x)/(2)+sqrt(3-3x^(2))/(2)}=(pi)/(3) .

3 sin ^(-1)((2 x)/(1+x^(2)))-4 cos ^(-1)((1-x^(2))/(1+x^(2))) +2 tan ^(-1)((2 x)/(1-x^(2)))=(pi)/(3) ( then ) x=

int_(-(1)/(sqrt(3)))^(-(1)/(sqrt(3)))(x^(4))/(1-x^(4))cos^(-1)((2x)/(1+x^(2)))dx

IF 3 sin^(-1)((2x)/(1+x^(2)))-4cos^(-1)((1-x^(2))/(1+x^(2)))+ 2tan^(-1)((2x)/(1-x^(2)))=(pi)/3 then x=

int_(-1/2)^(1/2) [sin^(-1)(3x-4x^(3)) - cos^(-1) (4x^(3)-3x)] dx =

cos^(-1)((x^(2))/(6)+sqrt(1-(x^(2))/(9))sqrt(1-(x^(2))/(4)))=cos^(-1)((x)/(3))-cos^(-1)((x)/(2)) hold for all x belonging to