IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

Mr.IITIAN007

Hey Hey guys ! how can you say f ( x ) = sinx cosx is continuous ?

DON007

hey yaar....

as f(x) = sinx cosx

this can be written as ....

f(x) = (sin 2x )/2.............as sin 2x =2sin x cosx.....

okk

now as sin x ...........is continuous everywhere........therefore.........

sin2x will be continuous, and as sin2x is continuous .......therefore

sin 2x /2 will be continuous.........

therefore f(x) will be continuous....

ok....

hope u have understood....

thanku

Mr.IITIAN007

Hey friend but what about the cos x part.If I write sin2x=2sinx cosx then I have to prove the continuity for cos x .......that is possible ...but how I want to know !

priyesh

since sinx & cosx are two continuous functions for all x belonging to R

therefore there sum , difference , product will be continuous as well

If f & g are be two continuous functions at x = a then

f + g , f - g , f * g are also continuous at a

f/g is also continuous provided g(a) not equal to 0

The above rule is very important so learn it

i'm also attaching the graph of the function

hope you understood

cheers

Mr.IITIAN007

oh yeah ! I should have known it . In fact I have found many more rules like those useful to solve other problems.Thanx man , you got my salute.

neeraj_agarwal_1990

sinxcosx= 1/2sin2x...u can easily draw its graph...similar to sinx...
range=[-1/2,1/2] and period = pi

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