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AP EAMCET202120 Aug 2021Evening ShiftMathematicsDifferentiationActual

If y = sin ( sin x ) and y '' + f ( x ) · y ' + g ( x ) · y = 0 , then f ( x ) · g ( x ) =

Options

  1. A1 2 sin ( 2 x )
  2. B1 2 cos ( 2 x )
  3. Csin ( 2 x )
  4. Dcos ( 2 x )

Correct answer

A. 1 2 sin ( 2 x )

Step-by-step solution

Since y = sin ( sin x )   . . . i Differentiating w.r.t. x by chain rule y ' = cos sin x . cos x   . . . i i Again differentiate w.r.t. x ⇒ y '' = - sin sin x × cos 2 x - sin x × cos sin x ⇒ y '' = - sin sin x × cos 2 x - sin x × cos sin x . cos x cos x by equation i and i i ⇒ y '' = - cos 2 x . y - tan x . y ' ⇒ y '' + tan x . y ' + cos 2 x . y = 0 Since we are given that y '' + f ( x ) · y ' + g ( x ) · y = 0 then by comparison f x = tan x ,   g

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