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

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

Text Solution

AI Generated Solution

To show that \(\frac{dy}{dx} = -\frac{y}{x}\) given \(x = \sqrt{a^{\sin^{-1} t}}\) and \(y = \sqrt{a^{\cos^{-1} t}}\), we will follow these steps: ### Step 1: Define the variables We have: \[ x = \sqrt{a^{\sin^{-1} t}} \quad \text{and} \quad y = \sqrt{a^{\cos^{-1} t}} \] ...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Concept Application 3.5|16 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Concept Application 3.6|8 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Concept Application 3.3|10 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Matrix Match Type|5 Videos

  • DOT PRODUCT

    CENGAGE ENGLISH|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)), y=sqrt(a^(cos^(-1)t)) , show that (dy)/(dx)=-y/x

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

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

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

For t in (0,1), Let \x= sqrt( 2 ^(sin^(-1)(t))) and y=sqrt(2 ^(cos^(-1)(t))) then 1+ ((dy)/(dx))^(2) equals :

If x=sqrt(a^(sin^(-1)t)),y=sqrt(a^(cos^(-1)t) , a >0 a n d -1 < t < 1 , show that (dy)/(dx)=-y/x .

If y=sqrt(x)^(sqrt(x)^(sqrt(x)^dotoo)) , show that (dy)/(dx)=(y^2)/(x(2-ylogx)) .

If sqrt(1-x^(2)) + sqrt(1-y^(2))=a(x-y) , show that (dy)/(dx)= (sqrt(1-y^(2)))/(sqrt(1-x^(2)))