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

Problem

cot(x)*sin(x)−sin(π/2−x)+cos(x)

Solution

1. Apply the cotangent identity to rewrite cot(x) in terms of sine and cosine.

cot(x)=cos(x)/sin(x)

2. Substitute and simplify the first term of the expression.

cos(x)/sin(x)⋅sin(x)=cos(x)

3. Apply the cofunction identity to the second term, sin(π/2−x)

sin(π/2−x)=cos(x)

4. Combine the simplified terms back into the original expression.

cos(x)−cos(x)+cos(x)

5. Perform the addition and subtraction to find the final result.

cos(x)−cos(x)+cos(x)=cos(x)

Final Answer

cot(x)*sin(x)−sin(π/2−x)+cos(x)=cos(x)

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