Home
Class 12
MATHS
If x = sqrt(a^(sin^(-1)t)) and y= sqrt(a...

If `x = sqrt(a^(sin^(-1)t))` and `y= sqrt(a^(cos^(-1)t)` show that `(dy)/(dx)= -y/x`.

Text Solution

Verified by Experts

`x=sqrt(a^(sin^(-1)t)),y=sqrt(a^(cos^(-1)t))`
`"or "xcdoty=sqrt(a^(sin^(-1)t+cos^(-1)t))=sqrt(a^(pi//2))`
Differentiating w.r.t. x, we get
`x(dy)/(dx)+y=0`
`"or "(dy)/(dx)=(-y)/(x)`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Concept Application 3.5|16 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Concept Application 3.6|8 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Concept Application 3.3|10 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 Videos

  • DOT PRODUCT

    CENGAGE PUBLICATION|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

If x=sqrt(a^(sin^(-1)t)), y= sqrt(a^(cos^(-1)t)) , show that (dy)/(dx)= -(y)/(x) .

If x=sqrt( a^(sin^(-1)t)) and y=sqrt( a^(cos^(-1)t)) find dy/dx

If x^2 = a^(sin^(-1)t) and y^2= a^(cos^(-1)t) then show that (dy)/(dx)=-y/x .

If x=(sin^(3)t)/(sqrt(cos 2t)) and y=(cos^(3)t)/( sqrt(cos 2t)) , show that (dy)/(dx)=0 at t=(pi)/(6) .

(dy)/(dx)=sqrt(y-x)

If x-sqrt(a^(2)-y^(2))=a" log"(a-sqrt(a^(2)-y^(2)))/(y) , show that, (dy)/(dx)=(y)/(sqrt(a^(2)-y^(2)))

If y = sqrt(x/(a))-sqrt(a/(x)) show that 2xy (dy)/(dx)=(x)/(a)-(a)/(x)

If y = sqrt(x/(m))+sqrt(m/(x)) show that 2xy (dy)/(dx) = (x)/(m) - (m)/(x) *

If y= tan^(-1)((a cos x-b sin x)/(b cos x+a sin x))" show that, " (dy)/(dx)= -1 .

If x^(2)+y^(2)=t+(1)/(t) and x^(4)+y^(4)=t^(2)+(1)/(t^(2)) then show that (dy)/(dx)=-(y)/(x) .