IGNOU BMTC 133 2026 - Prove that .

Question

Prove that $\sin x < x, \ x \in [0, \frac{\pi}{2}]$ .

20 Jan 2026

Answer :

Word Count : 225

Consider the function ( f(x) = x - \sin x ) for ( x \in [0, \frac{\pi}{2}] ). To show that (\sin x < x), it is sufficient to show that ( f(x) > 0 ) for all ( x \in (0, \frac{\pi}{2}] ). First, compute the derivative of ( f ): [ f'(x) = 1 - \cos x. ] Since ( \cos x \in [0,1] ) for ( x

___ ______ _____ ________ ______ ________ ______ _____ ___ ______ ______.
_________ __________ _______ __________ ___ _________ ______.
_________ __________ __________ ______ ____ ________ ________.
__________ ______ _________ ________ _______ ____ _________ __________ __________ __________.
______ ___ __________ _________ ______ ____ ____ ___ ____ __________ ______.
___ __________ _________ ______ _______ _________ _________ ________ ______.
_________ __________ ______ _____ ___ ____.
_________ ______ _______ ___ ________ ________ ___ _______ __________.
________ __________ _______ ____ __________ ________ _________ ____ ______ ________ _______ ________.
________ ____ ____ _______ _______ _____ _________ ___ ______ ___ _______ _________.
________ __________ ____ __________ ______ _____ _________ ________ ___ ______.
_________ ____ ______ ___ ________ _______ ________ ___ _____.
________ ____ ______ _________ __________ _____ __________.
______ ____ _____ ______ _______ _____ ________ ___ _____ ___ ___.
__________ ____ _______ ____ __________ _______ ____ _____ ________ ________.
__________ _____ ________ _________ _________ ___ _________ _____ ___ _________ _________.
______ ______ _____.

IGNOU ACADEMY

Your IGNOU journey, made easier.