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Question

If the functions f(x)=sin(x+a) and g(x)=bsinx+ccosx satisfy f(0)=g(0) and f′(0)=g′(0) then

A
b=π2
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B
b=cosa
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C
c=sina
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D
c=cosa
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Solution

The correct options are
B b=cosa
D c=sina
Given, f(x)=sin(x+a)
and g(x)=bsinx+ccosxf(0)=g(0)sina=cf(x)=cos(x+a)g(x)=bcosxcsinxf(0)=g(0)cosa=b

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