Simplify tan(x)csc(x)

Problem

tan(x)*csc(x)

Solution

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

tan(x)*csc(x)=sin(x)/cos(x)⋅1/sin(x)

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

sin(x)/(cos(x)*sin(x))=1/cos(x)

3. Apply the reciprocal identity 1/cos(x)=sec(x) to reach the simplest form.

1/cos(x)=sec(x)

Final Answer

tan(x)*csc(x)=sec(x)

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