sin^(-1)((x^(2))/(4)+(y^(2))/(9))+cos^(-1)((x)/(2sqrt(2))+(y)/(3sqrt(2))-2)" is "

y=sin^(-1)((x)/(sqrt(1+x^(2))))+cos^(-1)((1)/(sqrt(1+x^(2))))

sin^(-1)(x^2/4+y^2/9)+cos^(-1)(x/(2sqrt2)+y/(3sqrt2)-2)

y = sin^(-1)(x/sqrt(1+x^2)) + cos^(-1)(1/sqrt(1+x^2))

If tan^(-1)x+cos^(-1)((y)/(sqrt(1+y^(2))))=sin^(-1)((3)/(sqrt(10))) , then

(2)/(sqrt(x))+(3)/(sqrt(y))=2 and (4)/(sqrt(x))-(9)/(sqrt(y))=-1

{:((2)/(sqrt(x))+ (3)/(sqrt(y)) = 2),((4)/(sqrt(x))-(9)/(sqrt(y)) = -1):}

If I=int(sin x+sin^(3)x)/(cos2x)dx=P cos x+Q log|f(x)|+R then (a)P=(1)/(2),Q=-(3)/(4sqrt(2))(b)P=(1)/(4),Q=(1)/(sqrt(2)) (c) f(x)=(sqrt(2)cos x+1)/(sqrt(2)cos x-1)(d)f(x)=(sqrt(2)cos x-1)/(sqrt(2)cos x+1)

If y=cos^(-1){(2x-3sqrt(1-x^(2)))/(sqrt(13))}, find (dy)/(dx)

If y=y(x) is the solution of the equation e^(sin y) cos y""(dy)/(dx) +e^(sin y) cos x = cos x,y (0)=0, then 1+y ((pi)/(6)) +( sqrt(3))/(2) y((pi)/(3)) +(1)/( sqrt(2)) y((pi)/(4)) is equal to

IF y=cos^2((3x)/2)-sin^2((3x)/2) ,then (d^2y)/(dx^2) is: a) -3sqrt(1-y^2) b) 9y c) 3sqrt(1-y^2) d) -9y