Simplify tan(x)(cot(x)-cos(x))

Problem

tan(x)*(cot(x)−cos(x))

Solution

1. Distribute the tan(x) term to both terms inside the parentheses.

tan(x)*cot(x)−tan(x)*cos(x)

2. Apply reciprocal identities by substituting cot(x)=1/tan(x) into the first term.

tan(x)⋅1/tan(x)−tan(x)*cos(x)

3. Apply quotient identities by substituting tan(x)=sin(x)/cos(x) into the second term.

1−sin(x)/cos(x)⋅cos(x)

4. Simplify the expression by canceling the common cos(x) factors in the second term.

1−sin(x)

Final Answer

tan(x)*(cot(x)−cos(x))=1−sin(x)

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