Q. 84.2( 11 Votes )

Discuss the conti

Answer :

Let f(x) = cos x


Formula used:


f(x) is continuous at x = c where c is any real number


if L.H.L = R.H.L = f(c)



Take L.H.L




Put x = c – h



x c c – h c h c – c h 0




{ cos (A – B) = cos A cos B + sin A sin B}




= cos c (1) + (0) sin c


= cos c………………(1)


Take R.H.L




Put x = c + h



x c c + h c h c – c h 0




{ cos (A + B) = cos A cos B – sin A sin B}




= cos c (1) – (0) sin c


= cos c………………(2)


f(x) = cos x


f(c) = cos c………………(3)


From (1), (2) and (3):


L.H.L = R.H.L = f(c)


f(x) is continuous for any real number


Hence, cos x is continuous


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