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

sin^(- 1)x+sin^(- 1)y=cos^(- 1) (sqrt(1-x^2) sqrt(1-y^2)-xy) if x in [0,1], y in [0,1]

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

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

Find (dy)/(dx) in the following: y=sin^(-1)(2x sqrt(1-x^(2))),-(1)/(sqrt(2))

sin^(-1)x+sin^(-1)y=cos^(-1)(sqrt(1-x^(2))sqrt(1-y^(2))-xy) if x in[0,1],y in[0,1]

Prove the following: sin^-1x-sin^-1y = sin^-1[x(sqrt(1-y^2))-y(sqrt(1-x^2))]

sin^(-1)x+sin^(-1)y=cos^(-1)""{sqrt((1-x^(2))(1-y^(2)))-xy}

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

f(x)=sqrt(sin(cos x))+ln(-2cos^(2)x+3cos x+1)+e^(cos^(-1))((2sin x+1)/(2sqrt(2sin x)))