How do you simplify #(cos(-x))/(tan(-x))-sin(x)#?

1 Answer
Dec 5, 2017

Answer:

#-1/sin(x)#

Explanation:

Things to remember
#color(white)("XXX")color(red)(cos(-x)=cos(x))#

#color(white)("XXX"color(blue)(tan(-x)=-tan(x))#

#color(white)("XXX")color(green)(tan(x)=sin(x)/cos(x))#
and
#color(white)("XXX")color(magenta)(cos^2(x)=1-sin^2(x))#

#color(red)(cos(-x))/color(blue)(tan(-x))-sin(x)#

#color(white)("XXX")=color(red)(cos(x))/(color(blue)(-tan(x)))-sin(x)#

#color(white)("XXX")=color(red)(cos(x))/(-color(green)((sin(x))/(cos(x))))-sin(x)#

#color(white)("XXX")(-(color(red)(cos(x))) * (color(green)(cos(x))))/(color(green)(sin(x)))-sin(x)#

#color(white)("XXX")=(-color(magenta)(cos^2(x)))/(color(green)(sin(x)))-sin(x)#

#color(white)("XXX")=(-(color(magenta)(1-sin^2(x))))/color(green)(sin(x))-sin(x)#

#color(white)("XXX")=(sin^2(x)-1)/color(green)(sin(x))-(sin^2(x))/sin(x)#

#color(white)("XXX")=-1/sin(x)#