Simplify sin(x)cos(x)sec(x)csc(x)

Problem

sin(x)*cos(x)*sec(x)*csc(x)

Solution

1. Identify the trigonometric identities for the reciprocal functions.

2. Substitute the identities sec(x)=1/cos(x) and csc(x)=1/sin(x) into the expression.

sin(x)*cos(x)⋅1/cos(x)⋅1/sin(x)

3. Rearrange the terms to group the functions with their reciprocals.

sin(x)/sin(x)⋅cos(x)/cos(x)

4. Simplify the expression by canceling the common terms in the numerator and denominator.

1⋅1=1

Final Answer

sin(x)*cos(x)*sec(x)*csc(x)=1

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