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Discuss the continuity of the following functions :
f(x) = sin x – cos x
Idea : If f and g are two functions whose domains are same and both f and g are everywhere continuous then :
i) f + g is also everywhere continuous
ii) f – g is also everywhere continuous
iii) f*g is also everywhere continuous
∵ f(x) = sin x – cos x
It is a purely trigonometric function
As sin x is continuous everywhere and cos x is also continuous everywhere for all real values of x
As f(x) is nothing but difference of two everywhere continuous function
∴ f(x) is also everywhere continuous.
We can see this through its graph which shows no point of discontinuity.
Fig : plot of sin x + cos x