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If siny=xcos(a+y) , then (dy)/(dx) is eq...

If `siny=xcos(a+y)` , then `(dy)/(dx)` is equal to (a)`(cos^2(a+y))/(cosa)` (b) `(cosa)/(cos^2(a+y))` (c) `(sin^2y)/(cosa)` (d) none of these

Text Solution

AI Generated Solution

To find \(\frac{dy}{dx}\) given the equation \( \sin y = x \cos(a + y) \), we will use implicit differentiation. Here’s a step-by-step solution: ### Step 1: Differentiate both sides with respect to \(x\) Starting with the equation: \[ \sin y = x \cos(a + y) \] ...
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Knowledge Check

  • If siny = x sin (a+y) , then dy/dx is equal to

    A
    `{sin(a+y)}/(sin a)`
    B
    `{sin^2(a+y)}/(sin a)`
    C
    `{2sin(a+y)}/(sin a)`
    D
    `{sin^2(a+y)}/(sin y)`

  • If siny = x sin (a+y) , then dy/dx is equal to

    A
    `{sin(a+y)}/(sin a)`
    B
    `{sin^2(a+y)}/(sin a)`
    C
    `{2sin(a+y)}/(sin a)`
    D
    `{sin^2(a+y)}/(sin y)`

  • If y=sin[cos(x^(2))] then (dy)/(dx) is equal to

    A
    `-2xsinx^(2).cos(cosx^(2))`
    B
    `-2xsinx^(2).cosx^(2)`
    C
    `2x^(2)sinx^(2).cosx^(2)`
    D
    None of these

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    If sin^2x+cos^2y=1 then dy/dx is equal to

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

    If x=a cos 2t,y=b sin^(2)t then (d^(2)y)/(dx^(2)) is equal to

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