Simplify cot(pi/2-x)cos(x)

Problem

cot(π/2−x)*cos(x)

Solution

1. Apply the cofunction identity for the cotangent function, which states that cot(π/2−x)=tan(x)

cot(π/2−x)*cos(x)=tan(x)*cos(x)

2. Use the quotient identity to rewrite the tangent function in terms of sine and cosine.

tan(x)=sin(x)/cos(x)

3. Substitute the identity back into the expression.

sin(x)/cos(x)*cos(x)

4. Simplify the expression by canceling the common factor of cos(x) in the numerator and denominator.

sin(x)

Final Answer

cot(π/2−x)*cos(x)=sin(x)

Want more problems? Check here!