Simplify (tan(x))/(sin(x))

Problem

tan(x)/sin(x)

Solution

1. Use the identity for the tangent function, which is defined as the ratio of sine to cosine.

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

2. Substitute this identity into the original expression.

sin(x)/cos(x)/sin(x)

3. Rewrite the division as multiplication by the reciprocal of the denominator.

sin(x)/cos(x)⋅1/sin(x)

4. Cancel the common factor of sin(x) from the numerator and the denominator.

1/cos(x)

5. Apply the reciprocal identity for the secant function to reach the simplest form.

sec(x)

Final Answer

tan(x)/sin(x)=sec(x)

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