Question

If the functions $$\displaystyle f\left ( x \right )=\sin \left ( x+a \right )$$ and $$\displaystyle g\left ( x \right )=b\sin x+c\cos x$$ satisfy $$\displaystyle f\left ( 0 \right )=g\left ( 0 \right )$$ and $$\displaystyle {f}'\left ( 0 \right )={g}'\left ( 0 \right )$$ then

A
b=π2
B
b=cosa
C
c=sina
D
c=cosa

Solution

The correct options are B $$\displaystyle b=\cos a$$ D $$\displaystyle c=\sin a$$Given, $$f(x)=\sin(x+a)\quad$$and $$g(x)=b\sin x+c\cos x\\ f(0)=g(0)\Rightarrow \sin a=c\\ f'(x)=\cos(x+a)\\ g'(x)=b\cos x-c\sin x\\ f'(0)=g'(0)\Rightarrow \cos a=b$$Mathematics

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