Rewrite the expression as a single logarithm and simplify the result. (Hint: Begin by using the properties of logarithms.)

Question

ln(|cot(𝜃)|) + ln(|sin(𝜃)|)

Answer: _______

Answer 1

Logarithm Product Rule:

log_bM + log_bN = log_b(M · N)

Problem:

ln(|cot(θ)|) + ln(|sin(θ)|)

Solution:

= ln(|cot(θ)| · |sin(θ)|)

= ln(|cot(θ) · sin(θ)|)

= ln(|cos(θ)/sin(θ) · sin(θ)|)

= ln(|cos(θ)|)

Note: Don't forget the ABS function as the domain of ln(θ) is {θ | θ > 0}.

Answer 2

= ln [ cot * sin ]

= ln [ cos/sin * sin]

= ln [ cos]