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

Problem

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

Solution

1. Express all trigonometric functions in terms of sine and cosine using fundamental identities.

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

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

3. Cancel the common factors in the numerator and denominator.

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

4. Simplify the remaining terms after cancellation.

sin(x)/cos(x)

5. Apply the tangent identity to reach the final simplified form.

tan(x)

Final Answer

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

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