What is ln(cos(θ))-ln(sin(θ)) ?

The solution to ln(cos(θ))-ln(sin(θ)) is ln(cot(θ))

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simplify ln(cos(θ))-ln(sin(θ))

simplify

ln (cos (θ)) - ln (sin (θ))

ln (cot (θ))

Solution steps

ln (cos (θ)) - ln (sin (θ))

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (cos (θ)) - ln (sin (θ)) = ln (\frac{cos ( θ )}{sin ( θ )})

= ln (\frac{cos ( θ )}{sin ( θ )})

Rewrite using trig identities

= ln (cot (θ))

ln (\frac{15}{30})

ln (\frac{6.61}{0.3581})

- ln (s + 1) + ln (s + 3)

ln (\frac{r ^{2}}{r ^{1}})

lo g_{3} (7)

What is ln(cos(θ))-ln(sin(θ)) ?
The solution to ln(cos(θ))-ln(sin(θ)) is ln(cot(θ))