Evaluate the Limit

Problem

(lim_x→0)((cos(x)*tan(x))/x)

Solution

1. Rewrite the tangent function using the trigonometric identity tan(x)=sin(x)/cos(x)

2. Simplify the expression by canceling the cos(x) terms in the numerator.

(cos(x)*tan(x))/x=(cos(x)⋅sin(x)/cos(x))/x

(cos(x)*tan(x))/x=sin(x)/x

3. Apply the fundamental trigonometric limit theorem, which states that (lim_x→0)(sin(x)/x)=1

Final Answer

(lim_x→0)((cos(x)*tan(x))/x)=1

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