Simplify cos(x)csc(x)^2-cos(x)cot(x)^2

Problem

cos(x)*csc2(x)−cos(x)*cot2(x)

Solution

1. Factor out the common term cos(x) from both parts of the expression.

cos(x)*(csc2(x)−cot2(x))

2. Identify the Pythagorean identity that relates the cosecant and cotangent functions.

1+cot2(x)=csc2(x)

3. Rearrange the identity to find the value of the expression inside the parentheses.

csc2(x)−cot2(x)=1

4. Substitute the value of the identity back into the factored expression.

cos(x)*(1)

5. Simplify the resulting product.

cos(x)

Final Answer

cos(x)*csc2(x)−cos(x)*cot2(x)=cos(x)

Want more problems? Check here!