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If sin(a+y)+sina.cos(a+y)=0. Prove that...

If ` sin(a+y)+sina.cos(a+y)=0.` Prove that : `(dy)/(dx)=(sin^2(a+y)/(sina))`

A

`(sin^(2) (a +y))/(sin a)`

B

`(cos^(2) (a + y))/(cos a )`

C

`(sin^(2) (a + y))/(cos a )`

D

`(cos^(2) (a +y))/(sin a )`

Text Solution

Verified by Experts

The correct Answer is:
A
` x = - sin a . Cot (a + y)`
On differentiating both sides w.r.t.y, we get
` (dy)/(dx) = sin a. "cosec"^(2) (a + y)`
` therefore (dy)/(dx) = (sin^(2) (a + y))/(sin a )`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -EXERCISE 1 (DERIVATIVE OF IMPLICIT FUNCTION)
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  3. If x^(4) + y^(4) = 3xy, "then " (dy)/(dx) is equal to

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  4. If x = (y)/(sin y), then (dy)/(dx)

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  5. If y = x^(2). e^(xy) then derivative of y is

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  6. If xsqrt(1+y)+ysqrt(1+x)=0, for, -1<x<1,prove that (dy)/(dx)=-1/((1+x)...

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  7. यदि cosy=x cos(a+y), तथा cos a ne +-1, तो सिध्य कीजिये कि (dy)/(dx)=(c...

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  8. If 3 sin (xy) + 4 cos (xy) = 5 , " then " (dy)/(dx) is equal to

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  9. If sin^(2) x + cos^(2) y = 1 , " then " (dy)/(dx) is equal to

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  10. If sin(a+y)+sina.cos(a+y)=0. Prove that : (dy)/(dx)=(sin^2(a+y)/(sina...

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  11. Let y be an implicit function of x defined by x^(2x)-2x^xcot y-1=0. ...

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  12. If 2^x+2^y=2^(x+y), then (dy)/(dx) is equal to

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  13. If x^(2//3) + y^(2//3) = a^(2//3) , "then" (dy)/(dx) is equal to

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  14. If x=(1+logt)/(t^2),\ \ y=(3+2logt)/t ,\ \ find (dy)/(dx) .

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  15. If x=(1+logt)/(t^2),\ \ y=(3+2logt)/t ,\ \ find (dy)/(dx) .

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  16. If x=asec^3thetaa n dy=atan^3theta,fin d(dy)/(dx)a ttheta=pi/3dot

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  17. If x=a(cost+(logtan)1/2), y=asin t, then dy/dx is equal to

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  18. If x = t + (1)/(t) "and " y = t - (1)/(t) . "then" (dy)/(dx) is equa...

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  19. If x^2+y^2=(t+1/t) and x^4+y^4=t^2+1/t^2, then x^3y(dy)/(dx)=

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  20. If x=-a(theta-sin theta),y=a(1-cos theta), then (dy)/(dx) is

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