How do you simplify (cot(x))/(sin(x)-csc(x))?

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Answer 1 · 2018-02-19T00:14:13

The answer is #-secx#.

#cotx/(sinx-cscx)#

#(cosx/sinx)/(sinx-1/sinx)#

#((cosx/sinx)*sinx)/((sinx-1/sinx)*sinx)#

#((cosx/color(red)cancel(color(black)sinx))*color(red)cancel(color(black)sinx))/((sinx-1/sinx)*sinx)#

#(cosx)/(sin^2x-1)#

#cosx/(1-cos^2x-1)#

#cosx/-cos^2x#

#color(red)cancel(color(black)cosx)/-cos^color(red)cancel(color(black)2)x#

#1/-cosx#

#-1/cosx#

#-secx#