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