Determine the continuity of the function: f(x) = sin x + cos x?

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+2 Mathematics Continuity and Differentiability

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Hussam Uddin

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f(x) = sin x - sin (x+ 90), 2 sin (x + 45 ). sin (-45) = -2/sin 45. sin (x+45) = constant. sin (x+45 ) which is a continuous function for all values of x.
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Math, Sciences and Electrical Engineering

Both sin x and cos x are continuous functions. The sum or difference of continuous functions is also a continuous function. Alternate way is multiply and divide the equation by sqrt (2), sin x + cos x can be written as sqrt (2) * sin(x+45).
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