Simplify sin(x)+sin(x)cot(x)^2

Problem

sin(x)+sin(x)*cot2(x)

Solution

1. Factor out the common term sin(x) from the expression.

sin(x)*(1+cot2(x))

2. Identify the Pythagorean identity for the term inside the parentheses.

1+cot2(x)=csc2(x)

3. Substitute the identity into the expression.

sin(x)*csc2(x)

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

sin(x)⋅1/sin2(x)

5. Simplify the expression by canceling one factor of sin(x)

1/sin(x)

6. Apply the reciprocal identity to express the result as a single trigonometric function.

csc(x)

Final Answer

sin(x)+sin(x)*cot2(x)=csc(x)

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