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Question

If y=asinx+bcosx, then y2+(dydx)2 is a
  1. Function of x
  2. Function of y
  3. Function of x and y
  4. Constant

A
Function of x
B
Function of y
C
Constant
D
Function of x and y
Solution
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The correct option is D Constant
y=asinx+bcosx

dydx=acosxbsinx

y2+(dydx)2=(asinx+bcos)2+(asinxbsinx)2

=a2sin2x+2absinxcosx+b2cos2x+a2sinx2absinxcosx+b2sin2x

=a2sin2x+b2cos2x+a2sin2x+b2sin2x

=a2(sin2+cos2x)+b2(sin2x+cos2x)

=a2+b2 is a constant

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