Prove that the function defined by f(x) = tan x is a continuous f… - Vidyadip

Question

Prove that the function defined by f(x) = tan x is a continuous function.

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Answer

The function f (x) = tan x = $\frac{\sin x}{\cos x}$. This is defined for all real numbers such that cos x $\neq$ 0, i.e., x $\neq$ (2n +1) $\frac{\pi}{2}$. We know that both sine and cosine functions are continuous. Thus tan x being a quotient of two continuous functions is continuous wherever it is defined i.e, in its domain of definition.

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