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

Problem

cos(x)*tan(x)*csc(x)

Solution

1. Rewrite the tangent function in terms of sine and cosine using the quotient identity tan(x)=sin(x)/cos(x)

cos(x)⋅sin(x)/cos(x)⋅csc(x)

2. Rewrite the cosecant function in terms of sine using the reciprocal identity csc(x)=1/sin(x)

cos(x)⋅sin(x)/cos(x)⋅1/sin(x)

3. Cancel the common factors of cos(x) in the numerator and denominator.

sin(x)⋅1/sin(x)

4. Cancel the common factors of sin(x) in the numerator and denominator to find the final value.

1

Final Answer

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

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