- #1
ProfuselyQuarky
Gold Member
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I was supposed to simplify the expression ##\ln |\cot {x}|+\ln |\tan {x}\cos {x}|## and apparently it’s wrong. Where’s the mistake? Is it not simplified enough or . . . ?
##\ln |\cot {x}|+\ln |\tan {x}\cos {x}|##
##=\ln |\frac {\cos {x}}{\sin {x}}|+\ln |\frac {\sin {x}}{\cos {x}}\cdot \cos {x}|##
##=\ln |\frac {\cos {x}}{\sin {x}}|+\ln |\sin {x}|##
##=\ln |\frac {\cos {x}\sin {x}}{\sin {x}}|##
##=\ln |\cos {x}|##
If it’s really obvious, I’ll be happy with a hint. I thought that this was easy, but apparently I was mistaken?
##\ln |\cot {x}|+\ln |\tan {x}\cos {x}|##
##=\ln |\frac {\cos {x}}{\sin {x}}|+\ln |\frac {\sin {x}}{\cos {x}}\cdot \cos {x}|##
##=\ln |\frac {\cos {x}}{\sin {x}}|+\ln |\sin {x}|##
##=\ln |\frac {\cos {x}\sin {x}}{\sin {x}}|##
##=\ln |\cos {x}|##
If it’s really obvious, I’ll be happy with a hint. I thought that this was easy, but apparently I was mistaken?