Question

If the maximum and the minimum values of $\cos \left(\sin \left(\cos x\right)\right)$ are $a$ and $b$ respectively, then

• A. $a=\cos \left(\sin b\right)$
• B. $b=\cos \left(\sin a\right)$
• C. $a=b$
• D. $b=\cos a$

Answer 1

Answer: (B)

$b=\cos \left(\sin a\right)$

as we know-
maximum and minimum value of cosine function are 1 and 0 respectively.
so,maximum value of $\sin \left(\cos x\right)$ will be $\sin \left(1\right)$ ,at x=0
and, minimum value of $\sin \left(\cos x\right)$ will be $\sin \left(0\right)=0$ ,at $x=\frac{\pi }{2}$
$\cos \left(sin\left(cosx\right)\right)$ will be maximum when $\sin \left(\cos x\right)$ will be minimum and it will be minimum when $\sin \left(\cos x\right)$ will be maximum -
so,maximum value of $\cos \left(sin\left(cosx\right)\right)=\cos \left(0\right)=1=a$
and, minimum value of $\cos \left(sin\left(cosx\right)\right)=\cos \left(sin\left(1\right)\right)=b$
so we can write-
$b=\cos \left(\sin a\right)$