Verify the identity.cos(u) sec(u)tan(u) = cot(u)Use a Reciprocal Identity to rewrite the expression, and then simplify.

Sure, let's verify the identity step by step.

1. Start with the left side of the equation: cos(u) sec(u)tan(u)

2. We know that sec(u) is the reciprocal of cos(u), so sec(u) = 1/cos(u). Similarly, tan(u) is sin(u)/cos(u). Substitute these into the equation: cos(u) * (1/cos(u)) * (sin(u)/cos(u))

3. The cos(u) in the numerator and denominator will cancel out, leaving us with: sin(u)/cos(u)

4. sin(u)/cos(u) is the definition of tan(u), but we want to get to cot(u). We know that cot(u) is the reciprocal of tan(u), so we take the reciprocal of sin(u)/cos(u) to get cos(u)/sin(u)

5. Therefore, cos(u) sec(u)tan(u) simplifies to cot(u), verifying the identity.