If `"sec"^(-1)x="cosec"^(-1)y`, show that `1/(x^(2))+1/(y^(2))=1`

Solve sec^(-1) x gt cosec^(-1) x

If y=sin^(-1)x , show that (d^2y)/(dx^2)=x/((1-x^2)^(3//2))

If y= (sec^(-1)x)^(2) , prove that x^(2)(x^(2)-1) (d^(2)y)/(dx^(2)) +x(2x^(2)-1) (dy)/(dx) -2=0 .

If sec^(-1) x = cosec^(-1) y , then find the value of cos^(-1).(1)/(x) + cos^(-1).(1)/(y)

If y="cosec"^(-1)x ,\ \ x >1 , then show that x(x^2-1)(d^2y)/(dx^2)+(2x^2-1)(dy)/(dx)=0 .

If y=e^(acos^(-1)x),-1lt=x<1 , show that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)-a^2y=0

If y=e^(acos^(-1)x), -1lt=xlt=1, show that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)-a^2y=0 .

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))

If e^y(x+1)=1, show that (d^(2y))/(dx^2)=((dy)/(dx))^2 If y=sin(2sin^(-1)x), show that ((1-x^2)d^(2y))/(dx^2)=x(dy)/(dx)-4y

If y=e^(acos^(-1)x) , -1lt=xlt=1 , show that (1-x^2) (d^2y)/(dx^2)-x(dy)/(dx)-a^2y=0 .