How do you rewrite the expression as a single logarithm and simplify #lnabscott+ln(1+tan^2t)#?
1 Answer
Mar 16, 2018
# 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) | #
