Simplify sec(x)*(sin(x))/(tan(x))

Problem

sec(x)⋅sin(x)/tan(x)

Solution

1. Rewrite the trigonometric functions in terms of sine and cosine using the fundamental identities sec(x)=1/cos(x) and tan(x)=sin(x)/cos(x)

sec(x)⋅sin(x)/tan(x)=1/cos(x)⋅sin(x)/sin(x)/cos(x)

2. Simplify the fraction by multiplying the numerator by the reciprocal of the denominator.

1/cos(x)⋅sin(x)⋅cos(x)/sin(x)

3. Cancel the common terms sin(x) in the numerator and denominator.

1/cos(x)⋅cos(x)

4. Multiply the remaining terms to find the final simplified value.

cos(x)/cos(x)=1

Final Answer

sec(x)⋅sin(x)/tan(x)=1

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