Home
Class 12
MATHS
If siny=xsin(a+y), prove that (dy)/(dx)=...

If `siny=xsin(a+y),` prove that `(dy)/(dx)=(s in^2(a+y))/(sina)` .

Text Solution

AI Generated Solution

To prove that \(\frac{dy}{dx} = \frac{\sin^2(a+y)}{\sin a}\) given the equation \(\sin y = x \sin(a+y)\), we will follow these steps: ### Step 1: Start with the given equation We have: \[ \sin y = x \sin(a+y) \] ...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|102 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA|Exercise Solved Examples And Exercises|67 Videos

Similar Questions

Explore conceptually related problems

If y,=x sin(a+y), prove that (dy)/(dx),=(s in^(2)(a+y))/(sin(a+y)-y cos(a+y))

If y,=x sin(a+y), prove that (dy)/(dx),=(s in^(2)(a+y))/(sin(a+y)-y cos(a+y))

If y=x sin(a+y), prove that (dy)/(dx)=(sin^(2)(a+y))/(sin(a+y)-y cos(a+y))

If x sin(a+y)+sin a cos(a+y)=0, prove that (dy)/(dx)=(s in^(2)(a+y))/(sin a)

If x sin(a+y)+sin a cos(a+y)=0, prove that (dy)/(dx)=(s in^(2)(a+y))/(sin a)

If x sin(a+y)+sina.cos(a+y)=0 , then prove that (dy)/(dx) = (sin^(2)(a+y))/(sina)

If xcos(a+y)=cosy , then prove that (dy)/(dx)=(cos^(2)(a+y))/(sina) . Hence, show that sina(d^(2)y)/(dx^(2))+sin2(a+y)dy/dx=0 .

If cosy=xcos(a+y) , with cosa!=+-1 , prove that (dy)/(dx)=(cos^2(a+y))/(sina) .

If sin y=xsin (a+y) ,then (dy)/(dx)

If xy=4, prove that x((dy)/(dx)+y^(2))=3y