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in Continuity and Differentiability by (27.3k points)
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Discuss the continuity of the following functions : 

f(x) = sin x – cos x

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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

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