Simplify tan(x)csc(x)cos(x)

Problem

tan(x)*csc(x)*cos(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)*cos(x)=sin(x)/cos(x)⋅1/sin(x)⋅cos(x)

2. Cancel the common factors of sin(x) in the numerator and denominator.

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

3. Simplify the remaining expression by canceling the common factors of cos(x)

cos(x)/cos(x)=1

Final Answer

tan(x)*csc(x)*cos(x)=1

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