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

Problem

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

Solution

1. Rewrite the trigonometric functions sec(x) and tan(x) in terms of sin(x) and cos(x) using the reciprocal and quotient identities.

sec(x)=1/cos(x)

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

2. Substitute these identities into the original expression.

(sin(x)⋅1/cos(x))/(cos(x)⋅sin(x)/cos(x))

3. Simplify the numerator and the denominator separately.

Numerator: *sin(x)⋅1/cos(x)=sin(x)/cos(x)

Denominator: *cos(x)⋅sin(x)/cos(x)=sin(x)

4. Combine the simplified parts into a single fraction.

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

5. Divide by multiplying the numerator by the reciprocal of the denominator.

sin(x)/cos(x)⋅1/sin(x)

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

1/cos(x)

7. Apply the reciprocal identity to express the result in its simplest form.

1/cos(x)=sec(x)

Final Answer

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

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