# How do you rewrite the expression as a single logarithm and simplify #lnabscott+ln(1+tan^2t)#?

##### 1 Answer

Mar 16, 2018

#### Answer:

# ln |cott| + ln (1+tan^2t) -= ln |2csc(2t) | #

#### Explanation:

We use the rules of logarithms:

# log AB -= log A + log B #

So, we can write the expression as:

# ln |cott| + ln (1+tan^2t) -= ln ( |cott|(1+tan^2t) ) #

# " " = ln ( |cott(1+tan^2t)| ) #

# " " = ln |cost/sint 1/cos^2t| #

# " " = ln |1/sint 1/cost| #

# " " = ln |1/(sint cost) | #

# " " = ln |2/(2sint cost) | #

# " " = ln |2/sin(2t) | #

# " " = ln |2csc(2t) | #