Question

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

• A. $b=\frac{\pi }{2}$
• B. $b=\cos a$
• C. $c=\sin a$
• D. $c=\cos a$

Answer 1

Answer: (B), (C)

$b=\cos a$
$c=\sin a$

Given, $f\left(x\right)=\sin (x+a)$

and $g\left(x\right)=b\sin x+c\cos xf\left(0\right)=g\left(0\right)\Rightarrow \sin a=c{f}^{\prime }\left(x\right)=\cos (x+a)g^{\prime }\left(x\right)=b\cos x-c\sin x{f}^{\prime }\left(0\right)=g^{\prime }\left(0\right)\Rightarrow \cos a=b$